24577

Areas of compound circles

Teacher notes

Students should work in pairs or groups of three for this activity.

Materials required
Two A3 sheets per group.
One copy of pages 2, 3 and 4 per group.
Glue and scissors.

How to use the resource

Distribute the diagrams sheet (page 2). Students cut up the sheet and stick the diagrams
onto two A3 sheets – four per sheet. They then work out the area of the shaded parts and
write out their full method alongside each diagram.

When they have finished (or done as much as they can), distribute the workings sheet
(page 3) to match up with the diagrams. Students should compare their method to the
given methods, making any changes where appropriate. If changes are made they should
also make sure they change their final answers too.

Finally students are given page 4 with the numerical answers.

This means that students can check that they understand the method of finding the area
and also how to input the numbers into their calculators to get the correct numerical
answer.

Solutions (final answers to 1 d.p.)

52 78.5 cm2 25.1 cm2

Area square 242 576 cm2 Area large circle 82 201.06 cm2
Area circle 122 452.39 cm2 Area small circle 42 50.27 cm2
Shaded area 123.6 cm2 Shaded area 150.8 cm2

Area square 42 16 cm2

= 6.28 cm2 Area 19.6 cm2
Area semicircle =

Total area 22.3 cm2

Area 112 380.1 cm2 Area 152 706.9 cm2

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Areas of compound circles

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Areas of compound circles

8 4 4 2
2

5 11

5 24 12
4

15 4
2
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Page 3 of 4

Areas of compound circles

22

22

22

2 2

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