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

Year:  GCSE

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

Popular topics:   Area worksheets, Shape worksheets

Difficulty level:  

Worksheet Overview



Question: What do you call an alligator in a vest?

Answer: An investigator, of course.


Let's 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 is to be able to work out the area of these simple shapes.

Let's 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 semicircle.

To find the semicircle, find the area of the full circle: π x 3 x 3 =  28.27 then 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 semicircle: π x 5 x 5 = 78.54 cm² ÷ 2 = 39.27 cm²

Total area: 31.5 cm² + 39.27 cm² = 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

Try an activity or get started for free