Skip to content
MathsGenie logo
Open app

Course home

  1. GCSE
  3. Maths Edexcel
  5. Revision guides

Area of Compound Shapes

A compound shape is a shape made up of different shapes.

Here is a compound shape:

compound shapes 1

To work out the area of this shape we can split it into two rectangles.

There are two ways of splitting the shape into two rectangles. We can split the shape like this:

compound shapes 2

To find the area of the whole shape we will work out the area of the two rectangles and add them together.

To find the area of a rectangle we need to multiply the length by the width.

We know the length and the width of the bigger rectangle. We need to find a missing length of the smaller rectangle.

The height of the whole shape is 9 cm and the height of the bottom shape is 5 cm. To find the height of the top shape we need to take 5 away from 9
9 - 5 = 4
(The smaller rectangle is a square)

compound shapes 3

We now have all the information we need to calculate the areas.

The area of the large rectangle is 5 × 10 = 50 cm2

The area of the square is 4 × 4 = 16 cm2

The area of the whole shape is 16 + 50
16 + 50 = 66 cm2

We could have also split the shape like this:

compound shapes 4

We need to find the base of the rectangle on the left. The base of the whole shape is 20 cm and the base of the shape on the right is 4 cm.
We need to calculate: 10 - 4

10 - 4 = 6 cm

compound shapes 5

The area of the rectangle on the left is 5 × 6 = 30 cm2

The area of the rectangle on the right is 4 × 9 = 36 cm2

The area of the whole shape is 30 + 36
30 + 36 = 66 cm2

Here is another compound shape:

compound shapes 6

To find the area of the compound shape we need to split it into a rectangle and a triangle.

compound shapes 7

We know the length and width of the rectangle.

The area of a triangle = 1⁄2 × base × height

We need to work out the base and the height of the triangle.

The base is 12 - 6 = 6 cm
The height is 11 - 4 = 7 cm

compound shapes 8

The area of the rectangle = 12 × 4 = 48 cm2

The area of the triangle = 1⁄2 × 6 × 7
1⁄2 × 6 × 7 = 3 × 7 = 21 cm2

The total area = 48 + 21 = 69 cm2

Try these:

PreviousNext

How was this guide?

Teach Genie

Review Area of Compound Shapes by teaching Genie

Teach it back in your own words, spot gaps, and remember it better.

Start teaching
Genie and Baby Genie

Lesson

Recap your knowledge with an interactive lesson

7 minute activity

Start lesson

Area is the amount of space inside a 2D shape. It is measured in square units such as cm2cm^2cm2 and m2m^2m2.

For a rectangle, use A=l×wA = l \times wA=l×w. For a triangle, use A=12×b×hA = \frac{1}{2} \times b \times hA=21​×b×h, where the height meets the base at a right angle.

A compound shape is made from two or more simple shapes. Split it into rectangles and triangles you already know, then add joined parts or subtract cut-out parts.

Use the lengths written on the diagram, not a ruler. Many exam diagrams are not drawn accurately.

Questions

Put it into practice with exam-style questions

35 exam-style questions

Practice questions

Question 1

3 marks

Diagram NOT accurately drawn

Flashcards

Remember key concepts with flashcards

20 flashcards

Practice flashcards

What units are used to measure area?

Area of Compound Shapes Revision Guide

  1. GCSE
  2. /Maths
  3. /Area of Compound Shapes

Revision notes for Edexcel GCSE Maths Area of Compound Shapes. Open the guide for explanations and worked examples. Written against the Edexcel GCSE Maths (1MA1) specification, so the content matches what's examinable rather than general Maths background.

Revision guides

Practise questions

1 of 2

An L-shaped patio has an overall bottom length of 12 m and an overall height of 8 m. The top section is 5 m wide, and the vertical drop to the lower section is 3 m. What is the area of the patio?

Practise questions

1 of 1

A large rectangle measures 14 cm by 9 cm. A rectangular section measuring 6 cm by 4 cm is cut out from one corner. What area remains?

Practise questions

1 of 2

A compound shape consists of a 7 cm by 5 cm rectangle joined to a right-angled triangle with base 6 cm and perpendicular height 5 cm. What is its total area?

Practise questions

1 of 3

A large rectangle measures 10 cm by 7 cm. A smaller rectangle, 4 cm by 3 cm, is cut out from one of its corners. What is the area of the remaining compound shape?