Cambridge International Mathematics

Challenge

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208 Mensuration (length and area) (Chapter 9)

1 The rectangle contains 7 semi-circles and 2 quarter circles.

These circle parts are touching.

What percentage of the rectangle is shaded?

2 A regular hexagon and an equilateral triangle have the same perimeter. What is the ratio of their

areas?

3

Show that Area A+Area B =Area C.

4 In the figure shown, prove that the area of the annulus

(shaded) is^14 ¼l^2 , wherelis the length of a tangent to

the inner circle which meets the outer circle at A and B.

5 Prove that the shaded area of the semi-circle is equal to

the area of the inner circle.

6 The figure given represents a rectangular box. The

areas of 3 touching faces are 2 cm^2 , 4 cm^2 and 8 cm^2.

Determine the volume of the box.

7 Show that the two shaded regions have equal areas.

8

A

C

B

A

l B

4cmX

2cmX

8cmX

A thin plastic band is used to tie the seven plastic pipes together.

If the band is 50 cm long, what is the radius of each pipe?

IGCSE01

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y:\HAESE\IGCSE01\IG01_09\208IGCSE01_09.cdr Thursday, 23 October 2008 11:19:44 AM PETER