Take this quiz to show what you've learnt.

Fill in the gap: To work out the area of a __________ we need to know how many square units lie within its boundary.

Fill in the gap: Instead of counting square units within the rectangle, we can multiply the ________ and width to work out the rectangle’s area.

What number is represented by letter A?

What number is represented by letter B?

What number is represented by letter C?

Exploring rectangles quiz

﻿Hi, I'm Miss Kidd-Rossiter and I'm going to be taking today's lesson on rectilinear shapes. Before we get started, please make sure you're in a nice quiet place if you're able to be, you're free from all distractions, and you've got something to write with and something to write on. A ruler would be really helpful for today's lesson too. If you need to pause the video now to get anything sorted, then please do. If not, let's get going. So we're starting today's lesson with a try this activity then. How many different compound shapes can you make by joining the sides of the two rectangles below? It's going to really help you if you draw these out. So pause the video here and have a go at this task. Excellent work, well done. Did you come up with loads? 'Cause there are lots and lots and lots of answers here. So I can't possibly go through them all but I will model one way that you could have thought about it. So what I did was I picked the smaller shape that was purple. And I decided that I could put this into the other shape, onto the larger shape in two orientations. So either I could draw it this way or this way. So I started off doing it in this orientation, and I moved it all the way around the outside of my other rectangle. Then I repeated it with the shape in this orientation, and moved it around the outside of the other rectangle. So you can see, there are loads of options here. I can't cover them all but this is one way that you might have thought about it. So moving on to the connect activity then. In rectilinear shapes, all sides meet at right angles. That's a really important definition. So pause the video here and write that down. Excellent. Which of the following shapes then could be described as rectilinear? Once you've worked that out, have a go at thinking about Yasmin's statement. She says, "I think that all rectilinear shapes can be split into rectangles. Do you agree?" So pause the video now and have a go at this. Excellent, right, the first shape then, the one on the left-hand side, this one here, is this one rectilinear? Tell me now. Excellent, it is rectilinear. What about the second shape then? Is this one rectilinear? Tell me know. Excellent, yes, it is. What about the third one? Could that one be described as rectilinear? Excellent, no, it couldn't. And what about the last one? Could that one be described as rectilinear? No, it's not, well done. What did you think about Yasmin's statement then? Did you agree? Excellent, I agreed. This is true. All rectilinear shapes can be split into rectangles. So pause the video there and write that down 'cause it's really important. So we're going to have a look at this shape here. This is a hexagon and we are going to calculate the area of this hexagon by splitting it into rectangles. We've got a calculation on the screen there. 10 multiplied by 9, add 6 multiplied by 3. And we've got to explain how that calculation relates to the area. So pause the video now and think about it. Right, let's go through it then. So we're going to split our hexagon into two rectangles where I have done it there. Then we can see that the area of this shape here would be 10 multiplied by 9 centimetres to give us 90 centimetres squared. And the area of this shape here would be something multiplied by something. What are these two dimensions? What do we know? Tell me now. Excellent. We know that this one here has to be six centimetres because this part here is four centimetres and the full length is 10 centimetres. And we know that this part here must be three centimetres because we know that the full length is 12 centimetres and this part here is nine centimetres. So that means that the area of this rectangle here would be six centimetres multiplied by three centimetres, which gives us 18 centimetres squared. So we can see that we get the 10 times 9 here and then six times three in this rectangle here. Now I'd like you to pause the video and have a go at these questions that are on the board. So what splitting strategy could have led to the following calculations? Pause the video now and have a go at this task. Excellent, let's go through these together then. So the first one, you can see that I've split my hexagon there. I need to, first of all, work out my missing length, so I know that that length there is six centimetres. That means that the bottom rectangle will have an area of 12 multiplied by 6 and the top rectangle will have an area of four multiplied by nine. And then we would add them together to get the total area. Let's move on to the next one then. So this one, 10 multiplied by 12 take away three multiplied by four. How would I split my hexagon this time? Quite a tricky one this I think because we're not actually going to split the hexagon, we're going to make it into a larger rectangle. So when I do that, I know that this full rectangle would be 10 multiplied by 12 and then my smaller rectangle here has dimensions of three centimetres and four centimetres, so the area of that would be three times four. So to get the area of the hexagon, I would subtract the three multiplied by four from the 10 multiplied by 12. Let's look at the last one then. So we've got our hexagon again. And we've got this time to do nine multiplied by six, add four multiplied by nine, add six multiplied by three. And you can see how I've split it here. That means that this section here would be nine centimetres multiplied by six centimetres. This section here would be four centimetres multiplied by nine centimetres. And this section here would be six centimetres multiplied by three centimetres. The important point to note is that any of these methods would give you the same answer. So you can get used to working flexibly with splitting up the hexagons to find the areas in whichever way you can see best. We're now going to apply today's learning to the independent task. So pause the video now, navigate to the independent task, and when you're ready to go through some answers, resume the video. Good luck. Well done on the independent task. Good work. Let's go through some answers then. Which of these shapes are rectilinear? So we know that for them to be rectilinear, then all the sides must meet at right angles. So even though we've got right angles in all three shapes, so for example, there, there, there, there, in the first two, we also have non-right angles. So you can see those where I've marked them here. So those two, a and b, cannot be rectilinear, which means that only c is rectilinear. So well done on that. For the second one, you were firstly asked to fill in the missing dimensions. So looking at this side here, we look across and we can see it's seven there and it's parallel, so this is also going to be seven centimetres. Now, using that logic, if we look at this missing side here, what's it going to be? Call it out. Yes, that's right. So that's four centimetres here. And then have we missed any out? Yes, there's one more and that's this one here. Okay, so I know that this is 14. I already have three and six, which make nine, so this has to be five centimetres. Okay, and then you're asked to find the area and the perimeter of the shape. So to find the area, we know how to find the area of a rectangle. So we need to cut this into rectangles. Now, you might have done this in different ways. I found it easier to cut it into two rectangles like this. It's okay if you did it slightly differently. And I had six then multiplied by four, length times width is 24 centimetres squared. And then 7 times 14 is equal to 98 centimetres squared. Of course, to find the total area, I would need to add those up. So 24 added to 98 would have got me 122 centimetres squared. Like I said, you might have cut it up differently or done it slightly differently but you should have got the same answer of 122. For the perimeter, I grouped together some of the calculations to make it more efficient to calculate. Again, you might have done it differently. You might have actually added up each side individually, 14 add 7 add 5 add 4 add 6 add 7, add three and four, sorry. Or you might have grouped together some of these calculations. I looked at it as two lots of seven and four, which I've got from these sides, either side. Seven and four. And two lots of 14, which I know 14's across here, and if I add these sides up, it's also 14. But whatever way you did it, you should have got an answer of 50 centimetres. Moving on to the explore task now then. Two rectangles with a known area and perimeter are used to construct rectilinear compound shapes. For which of these shapes do you know the area? And can you find the perimeter of any of the shapes? So pause the video now and have a go at this task. Excellent, so let's go through this then. Let's do area first. So let's say that shape A has an area of A centimetres squared, 'cause we're told it's got a known area. And then shape B here has an area of B centimetres squared. Then for two of these shapes, this one's A centimetres squared and this one's B centimetres squared, so for this shape here, and this shape here, the area will just be A centimetres squared plus B centimetres squared, won't it? So we know the area of those two. And for this shape here, we can also work out the area because it will be the area of B centimetres squared, so the area of this shape, taking away the area of the other shape. So A centimetres squared. So for three of the shapes, we do know the area. For this shape here, this one, we don't know the area because the two rectangles are overlapping and we would need to know how much they're overlapping by in order to find the area. Similarly, for the perimeter, we would know the perimeter of the first shape and we would know the perimeter of the last shape because we know which parts are touching, and we've already seen in this unit that when we know which parts are touching, we can work out the perimeter. For shape two, if we knew how long the touching part was, this part here, then we could work out the perimeter but at the moment, we don't. And similarly, for the third shape, we don't know the perimeter because we don't know how much it's overlapping by. That's the end of today's lesson. So thank you so much for all your hard work. Please don't forget to go and take the end of lesson quiz so that you can show me what you've learned and hopefully I'll see you again soon. Bye.

Fill in the gap: Rectilinear shapes are polygons where all sides meet at a __________________.

Fill in the gap: We can find the area of rectilinear shapes by splitting the shape into two or more _________________.

Fill in the gap: One way in which the shape could be split is shown. The area of this shape can be calculated by the following calculation: 12 × ___ + 6 × 7

What is the area of this rectilinear shape?

Find the area (A) and perimeter (P) of this rectilinear shape.

Rectilinear shapes quiz

In this lesson, we will learn to calculate the area (and perimeter) of rectilinear shapes by 'combining' rectangles.

Maths

Y7 Maths

Key Stage 3

Year 7

Miss

Rectilinear shapes

Area of 2-D shapes

Geometry

THEME

UNIT

Describing perimeters

Describing areas

Cutting and combining shapes

Exploring rectangles

Area of parallelograms

Area of triangles

Further triangles

Find the perimeter of this shape.

A regular pentagon has a perimeter of 50mm. What is the length of one side of the pentagon?

Fill in the gap: Shape B has an area of 12 ____________ units.

Which letter represents the number 10?

Find the area of this parallelogram.

Find the area of this right-angled triangle.

A triangle has a base of 3cm and a perpendicular height of 4cm. What is its area?

Fill in the gap: A ______________  shape can be split into two or more other shapes.

Lesson overview:Rectilinear shapes

Core Content

Area of 2-D shapes: