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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



What do you call an alligator in a vest?


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.

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