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Find Compound Perimeters

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

'Find Compound Perimeters' worksheet

Key stage:  KS 4

Year:  GCSE

GCSE Subjects:   Maths

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

Curriculum topic:   Mensuration, Geometry and Measures

Curriculum subtopic:   Perimeter Calculations Mensuration and Calculation

Difficulty level:  

Worksheet Overview

rectangles with eyes

Question: Why was the area upset with the perimeter?

Answer: Because the area thought the perimeter always went around the problem.


Perimeter is the total distance taken up around the outside of a shape.

Can you think of examples of where perimeter might be used?

A good example is if you are fencing a field, or building a wall around something.  You will need to know the perimeter.


To find the perimeter simply add up all the lengths of each shape.


Example 1:


Compound shape             a compound shape


When you have a missing length, such as in this example, break it down as shown above.


Perimeter = 10 + 2 + 6 + 6 + 4 + 8 = 36 cm


Example 2:


compound perimeters         compound perimeters


Calculate the missing length.  If the slant height isn't given, you have to assume it is 4 cm.

Perimeter = 4 + 10 + 10 = 24 cm


Example 3:


compound perimeters


The length of the semicircle can be calculated by finding the circumference and dividing by 2.

Circumference = π x diameter

The circumference of the circle is π x 12 = 37.70 cm  (Take the value of pi as 3.142)

To get the circumference of the semicircle: 37.70 ÷ 2 = 18.85 cm

The missing length of the rectangle is 11 cm

12 + 11 + 11 + 18.85 = 52.85 cm


Let's move on to some questions now.

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