WAEC 2009 · Paper 2 · Q5

In the diagram, $ABCDEF$ is a triangular prism. $\angle ABC = \angle DEF = 90^\circ$ , $|AB| = 24$ cm, $|BC| = 7$ cm and $|CD| = 40$ cm.

(a)
Calculate $|AC|$ .
(b)
Calculate the total surface area of the prism.

Worked solution (try it first)

(a)

Triangle $ABC$ is right-angled at $B$ , so use Pythagoras: $|AC|^2 = 24^2 + 7^2$ .
$|AC|^2 = 576 + 49 = 625$ .
So $|AC| = 25$ cm.

(b)

The prism has two triangular ends and three rectangular faces.
Each triangle: $\frac12 \times 24 \times 7 = 84\text{ cm}^2$ .
Both ends give $168\text{ cm}^2$ .
The rectangles are $24 \times 40$ , $7 \times 40$ and $25 \times 40$ : $960 + 280 + 1000 = 2240\text{ cm}^2$ .
Total surface area $= 168 + 2240 = 2408\text{ cm}^2$ .

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