Loading please wait

The smart way to improve grades

Comprehensive & curriculum aligned

Try an activity or get started for free

Find the Area of Compound Shapes

In this worksheet, students will find the area of compound shapes, including circles.

'Find the Area of Compound Shapes' worksheet

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   AQA, Eduqas, Pearson Edexcel, OCR,

Curriculum topic:   Geometry and Measures, Mensuration

Curriculum subtopic:   Mensuration and Calculation Volume and Surface Area Calculations

Difficulty level:  

Worksheet Overview

Alligator

Question

What do you call an alligator in a vest?

Answer

An investigator of course.

 

Lets investigate how to find the area of compound shapes including circles.

Compound shapes are shapes made up of two or more simple shapes.

All we need to know is the area of these simple shapes. Lets recap.

Boy looking thoughtful

Area of a square/rectangle/parallelogram = base x height

Area of a triangle = base x height ÷ 2  OR 1/2 base x height

Area of a circle = π x radius x radius (πr²)  

The value of Π is usually taken as 3.14 or use the Π button on your calculator.

 

Example 1

Area of compound shape

Here you can separate this shape into a rectangle measuring 9 cm x 8 cm = 72 cm² and a semi circle.

To find the semi circle find the area of the full circle π x 3 x 3 =  28.27 now divide by 2 =  14.14 cm²

Now just add 72 cm² to 14.14 cm² = 86.14 cm²

 

Example 2

Area of compound shape

Area of the triangle = 7 x 9 = 63 cm² ÷ 2 = 31.5 cm²

Area of the semi circle = π x 5 x 5 = 78.54 cm² ÷ 2 = 39.27 cm²

Total area = 31.5 cm² + 39.27 cm ² = 70.77 cm²

 

Your turn to investigate.

What is EdPlace?

We're your National Curriculum aligned online education content provider helping each child succeed in English, maths and science from year 1 to GCSE. With an EdPlace account you’ll be able to track and measure progress, helping each child achieve their best. We build confidence and attainment by personalising each child’s learning at a level that suits them.

Get started
laptop

Try an activity or get started for free

  • educational
  • bettfutures
  • cxa
  • pta
  • era2016
  • BDA award
  • Explore LearningTuition Partner
  • tacm