Cambridge International Mathematics

Mensuration (solids and containers) (Chapter 11) 233

Example 3 Self Tutor

Find the surface area of the

square-based pyramid:

The figure has:

² 1 square base

² 4 triangular faces h^2 +4^2 =5^2 fPythagorasg

) h^2 +16=25

) h^2 =9

) h=3 fash> 0 g

Total surface area =8£8+4£(^12 £ 8 £3)

=64+48

= 112cm^2

Example 4 Self Tutor

Find the cost of erecting a 6 mby 4 m rectangular garden shed that is 2 m high

if the metal sheeting costs$15per square metre.

The shed: Net:

A 1 =6£ 4

=24m^2

A 2 =4£ 2

=8m^2

A 3 =6£ 2

=12m^2

) total surface area=A 1 +2£A 2 +2£A 3

=24+2£8+2£ 12

=64m^2

) cost=64£$15

= $960

5cm

4cm 4cm

hcm

5cm

8cm

8cm

8cm

2m

4m

6m

A 3

A 2 A (^1) 4m
6m
2m
6m
4m
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Y:\HAESE\IGCSE01\IG01_11\233IGCSE01_11.CDR Wednesday, 24 September 2008 4:20:28 PM PETER