Numbers and numerals

Axioms and arrays

Factors and multiples

Order of operations

Positive and negative numbers

Expressions, equations and inequalities

Angles

Classifying 2-D shapes

Constructing triangles and quadrilaterals

Coordinates

Area of 2-D shapes

Transforming 2-D figures

Prime factor decomposition

Conceptualising and comparing fractions

Manipulating and calculating with fractions

Ratio

Percentages

Different number systems

Sequences

Forming and solving equations

Forming and solving inequalities

Linear graphs

Accuracy and estimation

Algebra and problem solving

Ratio (8.6a)

Ratio, real life graphs, and rates of change

Direct and indirect proportion

Univariate data

Bivariate data

Famous maths problems

Angles and parallel lines

Angles in polygons

Bearings

Volume and surface area of prisms

Area review

Circles

FDP review (9.1a)

Probability

Sets and Venn Diagrams

Solving linear simultaneous equations algebraically

Solving linear simultaneous equations graphically

Angle review (9.5a)

Constructions, congruence, and loci

Pythagoras's theorem

Ratio review (9.7a)

Similarity and enlargement

Surds and trigonometry

Quadratic expressions (9.9)

Quadratic equations (9.10)

Indices and standard form

Growth and decay

Finance

Maths

Y8 Maths

Key Stage 3

Year 8

UNIT

In this lesson, we will be comparing the areas of rectangles and triangles. We will then draw triangles with identical areas to given rectangles.

Revisiting area: Rectangles and triangles

﻿Hello and welcome to this lesson on "Revisiting Area." Today we'll be looking at rectangles and triangles. My name is Mr. Maseko. Before you start this lesson, make sure you have a pen or a pencil and something to write on. Now, if you have those things let's get on with today's lesson. First try this activity, what other calculations can you write for these diagrams? Yasmin says she can write six times four, add three times four for this first diagram. So pause the video here and give this a go. Now that you've tried this, let's see what you've come up with. Here are some calculations that you could have come up with. For this first one, you could have had six add three times four, which can just be written as nine times four. For that second array, you could have had one time six, add three times four, which can simply be written as six add three times four. So what did these calculations actually represent? Well, you'll find that these calculations represent that areas of these arrays. Well, how do we know this? Well, if we just focus on this first calculation, six times four, so six multiplied by four is the area of that first rectangle and three times four is the area of that second rectangle. That's the same thing for this calculation. Well, one time six, well that's the area of that first rectangle, and three times four is the area of the second rectangle. And that's what we're looking at today, we're looking at areas of rectangles and triangles. Now, these are shapes drawn on the unit grid. Now, what does that mean? That each square is worth one units. So these shapes are drawn to scale. So by counting squares, what is the area of these two shapes? What do you notice? Pause the video here and give that a go. Now that you've tried this, let's see what you come up with. Well, you should have noticed that the area of that rectangle is 12 unit squares, so 12 unit squares. And that area of that triangle, if you count them we go one, two, three, four, five, six, seven, eight, and then you have nine, 10, 11, 12, and that's also 12 units squared. Those two shapes have the same area. Well, let's look at the side lengths. Well, the base of this rectangle is four units. So it's four units and the height is three units. So it goes up to three and the base is four. Whereas the base of this triangle is four units and the height is six units, but they have the same area. Why is that? We already know to work on the area of the rectangle, we do base multiplied by height, 'cause four times three gives us our 12 units squares, 'cause there's 12 unit squares in that rectangle. So how do we work out the area of a triangle. Well, I can hear you say it, keep that thought. Without counting squares, work out the area of this second triangle. So using that thought that you just came up with, how to work up an area of a triangle without counting squares, work out the area of that second triangle. Pause the video here and give that a go. Now that you've tried this, let's see what you come up with. Well, we already that this area is 12 units squares, this one is also 12 units squares. And then this one, well, how did you work that out? This one has, if you look, it has a base of four units and it has a height of six units, and the area was 12 units squares. How do you work it out? Well, you can see that the area of a triangle, so the area of a triangle, you notice is the base multiplied by the height divided by two. So what do you notice about the base and height lengths of rectangles and triangles that have the same area? What do you notice? Good, you can see that one of the lengths is the same and now for the triangles, the other length is double the length on the equivalent rectangle. Now, why is this? Why is it that for other the triangle, the other line has to be doubled to make the area the same. Good, because at the end to find the area of the triangle, we have to divide the base multiply by height by two. Now, why do we divide the base multiply by the height by two? Well, if you notice, a triangle is just half of the rectangle. So we've taken a rectangle and we've split it in half. That is why when we find the area of the triangle, we do the base multiply by the height, and then we divide that by two. Now has an independent task, on the grid below each rectangle, draw a triangle with the same area. Pause the video here and give this a go. Now that you've tried this, let's see what you could have come up with. Well, if you look, what's the area that first rectangle? Well, it has one, two, three, four, five, six, so that is six unit squares. Now, why am I saying six unit squares? Well, that's because we don't know whether this is a centimetre or a millimetre grid or a metre grid, but we know that it's to scale. So this can be any units. So it could be six centimetres squared, it could be six millimetres. Now, I could have a triangle with a base of two. Now if my base is two, what would my height be? Only one of lengths will be double, so my height would be six. Now triangle has the same area as a triangle, 'cause base times height, two times six divided by two, two times six is 12, divided by two, that gives you six unit squared. Same thing for that second one, well, the area of this is six times two, which is 12 units squared. So I could have one with the base of four at a height of six, and that'll give me an area of 12 units squared. Now, for this second one is five by three, so that's got an area of 15 units squared. So we could have a base of six and a height of five. We've got a height of five and a base of six, that is an area of 15 units squared. Now for this last one, we have a base of eight and a height of four, so that's 32. So I could have a base of eight and a height of eight and that would be my triangle with the equivalent area. One of the lengths of my triangle has to be double one of the lengths on my rectangle to make an equivalent triangle. Now really well done if you got all of these. Now, here are some parallelograms drawn on a unit grid. Draw some rectangles with the same area, what do you notice? How would you work out the area of a parallelogram without counting squares? Pause the video here and give that a go. Now that you've tried this, let's see what you come up with. Well, by counting squares, you should have noticed that the area of that first parallelogram, that was 20 units squared. If we want a rectangle with an area of 20, well, that is a four by five rectangle. That second one, that was 16 unit squared. Now, a rectangle that is you can have a two by eight rectangle. Now you've got a four by three parallelogram. Now there's a reason I really like about this time. I'm not going to count those squares. That parallelogram has an area of 12 units squared. So you could have had a four by three rectangle. Now why did I do that? How did I know that parallelogram had an area of 12 without counting both squares? Well, you could just say I made the question so I know the answers, but how else? I'll give you a clue the last one as well. A three by five, this one you should have counted as 15 units squared, which has the same as a three by five rectangle. Ah, what do you notice? Well, you should've noticed that the area of your parallelograms is just the base multiplied by the height. And if you notice, the base and the height are perpendicular to each other. A parallelogram it's just a rectangle. So if you look, we can actually prove that a parallelogram is just a rectangle. So if you take the end of your parallelogram, so if we just cut this end off and we take it and we paste it over here, look at what shape you have. That inside there, that is just a rectangle and it's what? It's that five by four rectangle. If I take that off, see, you've got up five by four, that parallelogram is just a rectangle that has been squished a bit. So I really hope that you've learned something in today's lesson something about working out the equivalent areas for triangles, rectangles and not even parallelograms. If you want to share some of your work, ask your parents or carer to share your work on Twitter tagging @OakNational and #LearnwithOak. Thank you for taking part in today's lesson.

In this lesson, we will be working out the area of compound shapes that can be deconstructed into triangles and quadrilaterals.

Revisiting area: Compound shapes

﻿Hello, and welcome to this lesson. My name is, Mr. Maseko. In this lesson we'll be looking at compound shapes, and their areas. Before you start this lesson make sure you have a pen, or a pencil and something to write on. Okay? Now that you have those things, let's get on with today's lesson. First, try this activity. This is a shape drawn on a unit grid. And on these grids here, I want you to draw a triangle and a rectangle that has the same area as the shape here. Pause the video here, and give this a go. Okay. Now let him tried best. Let's see what you come up with. Well, you should have realised that this shape has an area of twenty four units squared. Because you counted the squares in that you've got to twenty four. So you want a rectangle with an area of twenty four. So think of all effect to pads of twenty four. You can have a base or four, and a height of six. or eight and three, or 12 by two. I'm just going to go four and six. So we can have a base of four, and a height of................. six. And that's a rectangle with an area of twenty four. So four, five, six. Now we want a triangle with that same area, the how to work out the area of a triangle. Well, remember it is base times height divided by two. So our base for our triangle it'd be eight, then our height that can be six, because we know if we do eight times six divided by two, that would give us twenty four. So in today's lesson, we are looking at working out the areas of compound shapes. Now compound shapes, are shapes made from two or more shapes put together. Now without a unit grid, how would we work out the area of this shape? If we weren't, if we were just given the sidelines, well, what can you see in this compound shape? Well, you can see that this has, if I do this, we have a triangle in that, and we have two rectangles. So, we split this shape into three separate components. So you can see that this is a compound shape that's made from one triangle and two rectangles. Now am going to label this as one, two, and the triangle can be labelled as three. Now, rectangle one, what's the area of that rectangle? Well, it has a base of four, and a height of four. So four times four, that is sixteen centimetres squared, and then rectangle two. Well, that has a height of three. What is its baseline? Well we know that from there, to there is four centimetres, while the whole length is six. So that missing length is two centimetres. So that second rectangle is three by two, which is six centimetres squared. And now what about the triangle? Well, for the triangle, we have a base of two, a height. What's the height. Well, we've got three centimetres. We'll go one extra centimetre to get to four, and another centimetre. So that triangle is two by two. It's two times two, because the triangle, we divide by two. Why do you divide by two for triangle? Because the triangle is half a rectangle. SO it's two times two divided by two, which is two centimetres squared. So the total area of that shape. So the total, area.............. would be, you add all of those together, which is twenty four centimetres squared just by splitting our shape into its component parts. We were able to work out the area of the shape. Look at this trapezium, now a trapezium is a quadrilateral What does quadrilateral mean? It's a shape that has four sides, and it has a pair of parallel sides. So this is what a trapezium is. How many different ways can you come up with to work out the area of this trapezium. Now I want you to try this on your own first, before I give you a clue, pause the video here, and give this a go. Okay? Now that you've tried this, let's see what you could have come up with. And you could have say chopped this trapezium here. Say you cit that off. What you're left with is this. And then that piece that you've chopped off the end. Well, what can we do with it? We can take that piece, and then twist it round, and edit onto this side so that you end up with this rectangle. And it's a rectangle with a a height five. and a base of what's the base going to be? If you look that's our base we've chopped off the end, here. So what was that length that we chopped off? Well, that length there is two centimetres. Well, how do I know? Because, if you look at this, the middle is worth four centimetres, and on either side could going to make to eight centimetres on either side, we have two centimetres. So that baseline is, six centimetres. So, to work out the area of this trapezium with five by six, which gives us thirty centimetres squared. Okay. So that's one way we could have done this, and we get an area of thirty centimetres squared when we do this, but, we sort of just moved chopped a bit off, and moved into the other side, and then twisted it to make this a rectangle. But how do we know that this actually works? Because, I said that this two lines were equal. So they were both two and two, but does this work? Now, when we do stuff like this and that. If we can do multiple different ways, and get the same answer then we know that it's true. Now let's try it a different way. Another way you could have come up with this, I'm going to delete all of this, but I'll leave our target area. So we know that we're looking for an area of thirty centimetres squared That's what we worked out with the first method. Another way you could have done this, is you could have just replicated that trapezium, and now what do you have? Well, if you look at this shape that we have now, you make, so we've now made a parallelogram, and we know how to work out the area of parallelograms, and the area of parallelograms, it's just base times height. Well, what is the base of this parallelogram? We've got a length of eight, and then it could a trapezium, and flipped it over this length there is four, So eight by four like, it was a base of twelve centimetres and the height or the height is so five, centimetres so what we have is, that parallelogram has an area of twelve, times five, which gives us sixty centimetres squared, but we used two of our trapeziums to make that parallelogram. So if we do sixty divided by two, we get an area of thirty centimetres squared. Look, we've done it a different way. And we've got the same area. First, we made into a rectangle and I got an area of what?Thirty, we made it into a parallelogram by joining up two of our trapeziums. And we've got an area of 30 for one of our trapeziums, now what other ways could you have done this thinking about compound shapes. I've show you two ways. Well, again, let's delete all this. Another way you could have done this is, you can see that this trapezium is made from, a rectangle in the middle, and two identical triangles on either side. So that rectangle is four by five. This triangles are five by two. So the rectangle is worth twenty centimetres squared cause five times four the triangle, five times two divided by two, that is five centimetres squared. And that's also five centimetres squared. When you add all those together, 20 at five, at five, you get an area of thirty centimetres squared. And we've worked out the area of this trapezium ,three different ways. Now there are many other ways that you could have tried to work out the area of the trapezium. Now, for this independent task for each of these trapeziums I want you to draw two compound shapes with the same area. So pause the video here, and give that a go. Okay. Now that you've tried this, let's see what you've come up with. Well, the area of that first trapezium was twenty eight centimetres squared. Now you could have worked it out anyway, but I showed you three different ways. You could have worked them out the area of that second trapezium. Well that's one is twenty centimetres squared. Now you are to draw four different compound shapes. Two of them with an area of twenty eight, and two of them with an area of twenty. Now, you could have decided to combine any shapes that you wanted, but as long as the areas were twenty eight, now on a grid, it's nice and easy. You just have for the first shape, you have to cover twenty eight squares. The second shape you have to cover 20 squares. So if you count the number of squares in your shapes, the shape that you made, these ones have to have twenty squares in them. And these ones have to have twenty eight squares in them, now for this explore task. Can you use one of the ways that we figured out of working out that area of a, trapezium to show that the formula to work out the area of the trapezium is a plus b multiplied by the height, divided by two, pause the video here' and give that a go. Okay. Now that you've tried this, let's see what you could have come up with. We know that I have to divide by two at the end. So which one of our methods did we have to divide by two at the end for, well, we took our trapezium, and made it into a parallelogram. By twisting it round, and joining at the end. So this length is a that is b. And we know about the heights is h. Now that parallelogram that we've just made. What's the area of that parallelogram? What we know the baseline of that parallelogram is a plus b, and the height is h multiplied by the Heights. We know we want the area of our trapezium and our trapezium is made from two, and our trapezium is half of this parallelogram. So we know about you're going to what? Divide by two at the end. Now this is one way you could have shown this. Now you could have used the other methods to also do this, but turning it into a parallelogram was the easiest way to do this. Now that's it for today's lesson. Thank you so much for joining in. And I hope you learnt a lot about different ways we can work out the areas of compound shapes. I was splitting them, or turning them into other shapes that we know how to work up the areas off. I will see you again, next time. Bye for now.

In this lesson, we will be working out the area of circles when provided with a given radius.

Revisiting area: Circles

﻿Hello and welcome to this lesson on revisiting area, and today we'll be talking about the area of circles. Now before you start this lesson, make sure you have a pen or a pencil, and something to write on. Okay, now that you have all those things, let's get on with today's lesson. Firstly, try this activity. Now these are circles drawn on a unit grid. Now what that means is that each square is worth one unit. In this instance the units are centimetres. So by counting squares, can you state an approximate area for each of these circles and then what do you notice about that approximate area and the radius? Pause the video here and give this a go. Okay, now that you've tried this, let's see what you've come up with. Now for that first circle when you counted the squares, you should have gotten approximately 12 full squares. Now you may have gotten just over 12. But you should have approximately counted 12 four squares. For that second one, you should have approximately counted 27 full squares. And then for that last one, you should have gotten around... Can you see any relationship between the approximate number of full squares and the radius of this circles? Well, if you look at this, in that first one the number of full square is what? Six times the radius, and the second one, the number of full squares is nine times the radius. And then in that final one, the number of full squares is... Now right now nothing seems really obvious as jumping out as us, 'cause the first one is six, the second one is nine, the third one is 15. What do six, nine and 15 all have in common. Good, they're all multiples of three. So that first one that is two times three, that second one is three times three, and that last one is five times three. Are you I you spotting something? So if we look at this, the number of the approximate number of squares that we've counted. What is the radius? This instance radius was two times the radius again times three. And the second one is the radius, times the radius again, or times three. The last one is the radius, times the radius again times three. So the approximate number of squares. Now we going to to look at how we actually work out the actual area as we go on in today's lesson. Now it turns out to work out the area of a circle. The formula is pi times the radius squared. Now this number pi is approximately 3.142, and this is to three decimal places. Now pi is the ratio between the diameter of the circle. So it's the ratio between the diameter of the circle and the circumference of the circle. So it's a number that's constant for all circles. It's approximately 3.142. That's why we noticed here that the number of four squares was three times bigger, approximately about three times bigger than the radius squared. So in order to calculate the area, you always do pi times the radius squared. For a circle with a radius of eight centimetres. What is this area? Well, it would be pi times eight squared. pi times a squared eight squared. Eight squared is 64. So this will be written as 64 pi centimetres squared. Now we leave our answer here in terms of pi, because it's the most accurate answer. Now, here we are. Here we have another circle drawn on a new grid and a triangle also drawn on a unit grid. So which of these two has a bigger area? What do you think? Well, just by looking at it you may say, "Well, the triangle looks like it covers more area." Looks like it's covering more space. For what is the area of that triangle? Well, if you look the base is three and the height is one, two, three, four, five, six, seven, eight, and the height is eight. So the area of that triangle is three times eight divided by two which is 12 centimetres squared. We know centimetre squared 'cause we're on a centimetre grid. So each square is worth one centimetre. Now, would the circle with the radius of two have a smaller or larger area? Well, remember before we said the approximate number of squares in there was 12 squares, right? So this was 12 unit squares, should approximate area was 12 centimetres squared. But how do we know the circle has a bigger area? Good, I think that's the formula. The formula for the area for circle is pi times the radius squared. Now radius squared is four. So the area of this circle, the precise area of this circle pi times four, which is four pi centimetres squared. Now how do we know four pi is bigger than 12? Well, 12 is four times three, so 12 is four times three. And we know that pi is just a little bit bigger than three. So that's how we know four pi is bigger. Now here's an independent task, for these circles give you areas in terms of pi. And then on the second question, draw the largest triangle with integer side lengths, that has an area smaller than that of a circle with a radius of three. Pause the video here and give that a go. Okay, now that you've tried this, let's see what You've come up with, well, a circle with the radius of four centimetres. Well, that is pi times four squared, that is 16 pi centimetres squared. A circle the radius of eight. Well, that is pi times eight squared which is 64 pi centimetres squared. Now we want a triangle with integer side lengths with an area smaller than a circle with the radius of three. Well, what's that area of a circle the radius of three? hat's pi times three squared which is nine pi centimetres squared. Well, nine pi is bigger than 27. Because pi is just a little bit bigger than three. So nine times pi is bigger than mine times three. So we want a triangle with an area of 27. So what are the five lines of a triangle? So we're using a unit grid, you can just draw a triangle that has 27 squares in it, or you can try and work it out. Well, if the area is going to be 27, and we know that say one of the sides is nine, so one, two, three, four, five, six, seven, eight, nine. So nine times something divided by two is 27. Well, if you double 27 you get 54. So what nine times something gives you 54, so that's nine times... Good, that's nine time six. And if you join a nine by six triangle, you count the squares in there. It is 27 full squares. If you would worked out the area, it's nine times six divided by two, that is 27 centimetres squared. Now that is the largest triangle with integer side lengths, so one side is six centimetres and the other side is nine centimetres. Okay, now has an explore task. So you going to draw three different shapes with an area bigger than a circle with a radius of four centimetres. This has to be three different shapes. Pause the video here and give this a go. Okay, now that you've tried this, let's see what you come With. Well, the area of a circle with the radius of four, that is pi times four squared, which is what? 16 pi. And 16 pi, remember is about 16 times 3.142 approximately. So you want areas, that are constantly bigger than 48 to be sure, that you have an area that's bigger than the circle, because if you do an area of 49 more, you will notice if you actually calculate this, an area 49 is less than 16 pi 'cause 16 pi is about 50, rounded to the nearest whole number. So you want areas that are comfortably bigger than 48, So let's do one with an area of 60. So you can do a rectangle with an area of 60, so that is six by 10 rectangle, that has an area 60 and you know that that's bigger than 16 pi. Well, if we know that an area of 60 becomes 60 pi, we can draw a triangle with an area of 60. I'm not going to draw the triangle to scale we don't have enough space on the grid. So we can say not drawn to scale. So the hieght of 10 and a base of 12, and that triangle has an area of 60 centimetres squared. Again, we're looking for another shape with an area of 60 centimetres squared. So what else can we do? Well, we can do a parallelogram with a base of 10 and a height of six. one, two, three, four, five, six, and a height of six. Again, this is just going to go off the page just a little. There we go, and those are all three shapes with an area of 60 centimetres squared. And we know that 60 centimetres squared is comfortably bigger than 48. So we can definitely be sure that all of these are bigger than 16 pi. That's if we don't have a calculator to calculate how much 16 pi is exactly. Okay, now I really want that for getting through this lesson. And I look forward to seeing any work that you have to share and what shapes you came up with that were bigger than 16 pi. So if you want to share your work, ask your parent or carer to share welcome Twitter, tagging @OakNational and #LearnwithOak. I will see you again next time.

In this lesson, we will be looking at working out side lengths of various quadrilaterals and triangles when only given the area and 1 other measure of a shape.

Revisiting area: Working out side lengths when given area

﻿Hello, and welcome to this final lesson on revisiting area. In this lesson, we'll be looking at working out sidelines when given areas. My name is Mr. Masego. Before you start this lesson make sure you have a pen or a pencil and something to write on. Okay, now that you've got those things, let's get on with today's lesson. First try this activity, pause the video here and give this a go. Okay, now that you've tried this, let's see what you come up with. Well, give possible base and height lengths for a triangle with an area of 24. What could we have? Well, we want to get an area of 24, and we're not to work out the area of a triangle. It is base times height divided by two that gives us our area. So our base times height has to be double 24. 'Cause the only half it will get 24. So we could have had 12 by four to the base of 12 centimetres and a high to four centimetres. Well that would give you 12 times four is 48 divided by two is 24. What else could you have had, you could have had a triangle with eight by six. So as long as you get 48 so that you can half it to get 24, you'd have been fine. So for this trapezium, what would the a b and h length be to give us an area of 24? Well, how do you work out the area of a trapezium? Well we noticed a few lessons ago that the area of a trapezium can be given as a plus b times the height divided by two. So sort of like the triangle look, we've got something times the height divided by two. So a plus b times height, this has to be 48 because when you divide that by two you get 24. So you need two numbers that will multiply to give you 48. So we could have 12 and four and now a and b. So we can say the height is four a and b have to add together to give you 12. So any two numbers that add to give you 12. So you could have had seven and five 'cause seven plus five. Well, that gives you 12 times four is 48 divided by two that gives you 24. Now the easiest one of the three was the rectangle. And now in the rectangle, you could have read what? Just to get 24. You could have had at 12 times two or you could have had eight times three or six times four. So any two numbers are multiplied to give you 24. Now what we're looking at today is we're going to be working on sidelines. We'll have given an area and one other sideline. So here's the rectangle. And this rectangle has an area of 18 centimetres squared and we know the base is six. So what is the height of rectangle? Well, we know to work up the area rectangle is base times height. We know the basis six the area is 18. So 18 equal six times something and we know about would be three centimetres. We know that six multiply by three gives us 18. You could have done 18 divided by six to find out about the height was equal to three centimetres. Now rectangles are the easiest ones to do, because we're just looking for a factor pair. That makes our area. Now, what about triangles? Now in this triangle, we know that the base is four centimetres and we know that the area is 18 centimetres. How do you work out the area of a triangle? Good, it's base times height divided by two. So what would the height of this triangle be? What do the base and height have to multiply two? So that area is 18. Well, we're going to have to divide that by two. So something divided by two, gives you 18 and that would be? Good 36 cause double 18 is 36. So we know that the base in the heights have to base times the height have to multiply to give you 36. So four time something gives you 36. So the height will be good nine. So the height would be nine centimetres because four times nine is 36. So just look for factor pair that gives us 36. And we know that 36 divided by two is 18. Now here's a trapezium and we've been given a as seven b as five and the area is 30 and we have to workout what the height is. Now how would you do this? Remember the formula to work out the area of a trapezium, that a plus b times the height divided by how would you work out the height? Pause the video here and give this a go. Okay, now that you've tried this, let's see what you're going to come up with. What does this have to multiply to? Good that has to multiply to 60. Why does it have to multiply to 60? Because at the end we're going to divide it by two to get to our area of 30.. So it's the same as when we have a triangle. So the formula to work out the area of a triangle and the trapezium is very similar. On the triangle we just have base times height, but on the trapezium is that a plus b So you add the two parallel sides and then you multiply by the height and then divide by two. But that's the numerator of that fraction. So that part of the fraction has to be double the area. 'Cause when you divided, you will get what the area was. So you need two numbers multiply to give you 60. Well, we already know a plus b, a plus b is good 12. So we know that 12 multiplied by the height has to give us 60. So 12 times something gives us 60. So the height has to be good, the height has to be five centimetres. Okay, here's an independent task for you to try. These four shapes have the same area. So work out the Heights of the other three shapes? Pause the video here and give this a go. Okay, now that you've tried this, let's see what you've come up with. Well, you should have worked out the area of the rectangle, but is 40 centimetres squared, now full the triangle. Remember that is base times height divided by two. So the base times the height, well that has to equal 80 because 80 divided by two is 40. So eight times the height gives you 80. So the higher it has to be 10 centimetres. Now the area of a parallelogram. Well that is just base times height. Well, 10 times the height is 40. The height is four centimetres. The area for trapezium remember that is a plus b times the height divided by two. Well, a plus b that is 10 add 16 10 at six times, the height divided by two. Now that will be 16 times the height divided by two. That's 16 times height. What does that have to equal well 16 times of highest this has to 80 because 80 divided by two is 40. So 16 times the height is 80. So the height has to be five centimetres. Now here's an explore task. Workout the the length a, b and h for four trapeziums that have consecutive areas and what is consecutive mean? Consecutive means like three, four, five, six. So the areas have to be increasing by one each time. So what could be the values of a, b and h b for four trapeziums that have consecutive areas? Pause the video here and give that a go. Okay now that you've tried this, let's see what you come up with. Well, let's use the numbers that I gave to have an area of three. We know that a plus b times h has to be six because a plus b times the height divided by two is area. So do you have an area of three? a plus b times h has to be six because six divided by two. That gives you three. So we could have, what two numbers multiply to give you six? Well, three and two. So you could have the base as two a as one and the height as two, because two plus one is three times two, six divided by two that's three. So that gives an area to the area of this is three. Now we got an area four well, a plus b times height has to be eight so we could do two. So what we could do three, one and two, 'cause three plus one is four times two is eight and then divided by two that's four what about the next one. Well, we could do a base of four an a of one and a high of two, 'cause four plus one was five times two is 10 divided by two is okay. What about the next one? We could do five, one and two, because five plus one is six times two is 12 divide. Okay. What are you noticing? Whoa, we can see that the length a is staying the same all the way through. The length b, what's happening to that? Well, that's just increasing by one throughout. So starting at the huh, but what else can you see? Well, here when our height is two our areas are just what's a plus b when our height is two our areas are just a plus b. Cool, well in this sequence, what would the 20th area be? what would be the side lengths for the 20th trapezium? Well, how can you figure that out? Well what can we see if the area is three b is two the areas four b is three, the areas five b is four. So if the area is 20 well in this sequence, b would be 19 and a would be one and h would be two 'cause 19 plus one is 20 times two 40 divide by two 20. When you height is two your area is always just a plus b for your trapezium. Now some of you may have just picked different numbers for this. So you could have done a height of three. Like what did you notice when your height was three? What do you notice when your height is four? What do you notice when your height is five? Now if you want to share any of the discoveries that you made, ask your parent or carer to share what content to tagging at OakNational and #LearnOak Now, this was the last lesson in reviewing area. So look forward to any of the work that you sent in. Thank you very much for taking part. I will see you again next time.

Which of the following is larger than the area of a circle with a radius of 3cm?

Which of the following is smaller than the area of a circle with a radius of 4cm?

True or false: A circle with a radius of 2cm has a larger area than a rectangle with a base of 2cm and a height of 6cm.

How do you work out the area of a triangle?

How do you work out the area of a rectangle?

A rectangle with a height of 3cm and a base of 4cm has the same area as a triangle with a height of 3cm and a base of _________.

A compound shape is _____________________.

A trapezium has _______________.

What is the base of a parallelogram with an area of 24 and a height of 3?

What is the height of a triangle with an area of 55 and a base of 11?

This trapezium has an area of 25. Given that a=6 and b=4. Work out the height of the trapezium.

Unit Overview: Area review

Lessons:

Revisiting area: Rectangles and triangles

Revisiting area: Compound shapes

Revisiting area: Circles

Revisiting area: Working out side lengths when given area