NECO 2024 · Paper 1 · Q36

Plane mensuration
Trigonometric ratios

Calculate the area of trapezium $ABCD$ in the diagram, where $AB \parallel DC$ , $|AB| = 8\text{ cm}$ , $|DC| = 16\text{ cm}$ , $|BC| = 12\text{ cm}$ and $\angle BCD = 30^\circ$ .

Worked solution (try it first)

In the right-angled triangle at $C$ , the height is $h = 12\sin30^\circ$ .
As $\sin30^\circ = \frac12$ , $h = 6$ cm.
Area of a trapezium $= \frac12(a + b)h$
$= \frac12(8 + 16) \times 6$ .
So the area is $12 \times 6 = 72\text{ cm}^2$ , option C.

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