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

﻿Hi, I'm Mr Chan. And in this lesson, we're going to learn about the perimeter of polygons and compound shapes. Here's an example of how we can calculate the perimeter of a compound shape. A reminder, the perimeter is the distance around the outside of the shape. So that should be fairly straightforward. However, we do have some missing sides in this compound shape that we need to work out what the missing sides are. Firstly, before we can calculate the perimeter. So, let's have a look at this side length here, the vertical side length on the left hand side. Now I do know that they, the shape has a height of two on the bottom right hand side. And also from that too, it goes, Oh, woods another 10 centimetres. So if I add those two together, that would give me a total height of 12 centimetres. So horizontally, I know that the whole of the shape, has a nine centimetre base. Some of that is taken up horizontally by the four centimetres. I can see there. So that means the top side, that's horizontal there, must be five centimetres because I know that then five centimetres plus the four centimetres would equal the total nine centimetres. So now I'm in a position to calculate the whole perimeter of the compound shape. I can do that by adding all the sides together like that. And I would get a total of 42 centimetres. So that would be the perimeter of this compound shape. Here's some questions for you to try. Pause the videos, to complete the task. Resume the video, once you are finished. Here are the answers. So, in all this calculate the perimeter, of these compound shapes, I notice there are some missing side lengths, which you've got to work out first. So, think about what those missing sidelines are, and then once you've found those rounds, add them all up just to find the perimeter, the distance around the outside of the shape. 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. I'm pretty sure you worked out what Tom's mistake was. He obviously didn't work out the missing sides and include those in his perimeter calculation. So, it's very important to do that and not make the mistake that Tom made. So, once you work out what the missing sides are, I hope you got the answer of 66 kilometres. Here's another question for you to try. Pause the video to complete the task, resume the video once you're finished. In this question, we're told John has 132 metres of fencing and he wants to put fence around his field and we've got the diagram to use, to decide if he has enough fencing. So, in order to decide if he has enough fencing, we really just working out what the perimeter, of his field is. So if we're going to work out what the perimeter of his field is, we had to pull the side lengths, Just double check there are no missing side lengths, to calculate. And if we do that, we figure out the perimeter of the field, is actually 132 metres. So he doesn't have enough fencing. That's all for this lesson. Thanks for watching.

Find the perimeter of the compound shape.

Perimeter of polygons and compound shapes

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

Maths

Y10 Maths (Core)

Key Stage 4

Year 10

Y10 Maths (Foundation)

Area and Perimeter

Shape and Space (S)

THEME

UNIT

Area of rectangles, parallelograms and triangles

Area of a trapezium

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?

Work out the area of the rectangle.

Work out the area of the triangle.

Which of the following shapes does not have an area of 24 cm² ?

Lesson overview:Perimeter of polygons and compound shapes

Core Content

Area and Perimeter: