Work out the area of the trapezium.

Which of the following dimensions of a triangle have the same area as the trapezium in the diagram?

Area of a trapezium

﻿Hi, I'm Mr. Chan. And in this lesson, we're going to learn about the area of compound shapes. Here's an example of how we find the area of a compound shape. A reminder, a compound shape is just simply a shape made up of simpler shapes. So what we've got in front of us here is a trapezium and a rectangle. So it's basically a trapezium sitting on top of a rectangle. So I'm going to call those two shapes A and B, and I'm going to calculate those areas separately. And then at the end, add them together to find the total area of the compound shape. So the area of A, in terms of that, being a trapezium, I do need to know the length of the two parallel sides. So I'm missing the parallel side for the base of the trapezium but I know the rectangle has a base of 12. So that would mean that the trapezium also has a base of 12 because opposite sides of the rectangle are equal. The other side I need to know is the height. So the perpendicular height of the trapezium is five centimetres. And I've got that by subtracting the six centimetres away from the 11 centimetres. So I've got all I need to know in terms of finding the area of the trapezium. Now, the two parallel sides are eight and 12, which I add together. And the height of the trapezium is five centimetres. So I put that into the formula to work out the area of a trapezium. Calculated that to be 50 centimetres squared. The area of B is just simply the length times the width, 12 times six. So we get that area to be 72 centimetres squared. So the total area of the compound shape, we add those two areas together to get a total answer of an area of 122 centimetres squared. Here's some questions for you to try. Pause the video, to complete the task. Resume the video once you're finished. Here are the answers. So in part a we have a trapezium on top of rectangle. That's what makes that compound shape. So it's very much like the example that we covered previously. In part b, we have a rectangle with a triangle attached to it. Now the rectangle you can see has a length of 20 centimetres and a width of three centimetres. So you can calculate the area of that, pretty straight forward. And the rectangle is attached to a triangle. So the triangle has a base of seven centimetres which can use and a height of 12 centimetres. So it's important that you do use the perpendicular height with that. And don't forget to half the area for the triangle once you found it, because the area of a triangle is 1/2, multiplied by the base, multiplied by the height. Here's another question for you to try. Pause the video to complete the task. Resume the video once you're finished. Here's the answer. So Emily is trying to work out the area of this compound shape made up with two rectangles. Now her method there involves thinking about the rectangle as one large rectangle and subtracting the smaller rectangle imagining it's almost like cut out, if you like. So her method's really, really good. And some people do use this method. I like this method a lot. So basically she's found the area of the large rectangle and subtracted the area of the smaller rectangle, which measures nine millimetres by three millimetres. In this example, we need to calculate the area of the shaded region. So the shaded region I can see is made up of a triangle cut away from a parallelogram. So if I work out the area of those two and subtract one from the other, then I can work out the area of the shaded region. So let's work out the area of the parallelogram. That would be base multiplied by the height. So, 240 multiplied by 180, that gives an answer of 43,200 millimetres squared. The triangle is 1/2 multiplied by the base, multiplied by the height. So 1/2 multiplying 40 multiplying 40, to give an answer of 800 millimetres squared. So the shaded region, I would subtract the area of the triangle away from the parallelogram. So that gives me a calculation of 43,200 subtract 800. So a final answer of 42,400 millimetres squared for the area of the shaded region. Here are some questions for you to try. Pause the video to complete the task, resume the video once you're finished. Here are the answers. So in these questions, you've got to find the area of the shaded regions and a reminder that you find the area of the whole shape and then subtract the area of the shape that's not shaded. So in part a you've got a trapezium. And the unshaded part is a rectangle. So find the area of the trapezium and subtract the area of the rectangle. In part b, you've got a triangle and you would be subtracting the area of the smaller parallelogram in this question. In this example, we're told the area of the compound shape is 100 metres squared, and we've got to work out the length of the side marked x. So compound shapes, remember are just made up of simpler shapes and I can see that with this compound shape, we can split the compound shape up into two rectangles like this, by drawing the horizontal line there. Now that rectangle on the left, I can work out to be 30 metres squared. I get that from multiplying six and five together. So if I know that that's 30 metres squared, that must mean that the rest of the compound shape is 70 metres squared because I've been told the 100 metres squared is the total area. So I subtract that 30 away from the 100. That must be 70 metres squared. Now, that rectangle at the bottom it has a base of 14 metres. So in order to work out the length of the side marked x, I can just think about what do I need to multiply 14 by to get 70? I can calculate that by doing 70 divided by 14. That gives me an answer. The x must be five. Here are some questions for you to try. Pause the video, to complete the task. Resume the video once you're finished. Here are the answers. So in these questions, we have to find the missing lengths labelled x. So in part a, we've got a compound shape where we're told the area. And I'm going to imagine splitting up that compound shape up into two rectangles by drawing a vertical line. That lets me know that one of the rectangles measures 11 metres by five metres, which we can find the area of. That would be 55 metres squared. That leaves an area of 10.5 metres squared for the smaller rectangle. Now we can figure out one of the missing sides in the smaller rectangle, and that would be the horizontal side. That then allows you to figure out the vertical side for that rectangle, because you'll know that the area must equal 10.5 metres squared. Once you know that you can find what the length labelled x is. That's all for this lesson. Thanks for watching.

Work out the area of the compound shape.

The area of the compound shape is shown. Find the length of the side labelled x.

Area of compound shapes

In this lesson, students will find the area of compound shapes by dividing the shape up into simpler more easily recognisable shapes and finding the sum of their parts.

Lesson overview:Area of compound shapes

Core Content

Area and Perimeter: