WAEC 2020 · Paper 2 · Q4

(a)
The diagram shows a trapezium $ABCD$ in which $\overline{AB} \parallel \overline{DC}$ , $|AD| = 7.5\text{ cm}$ , $|AB| = 8\text{ cm}$ , $|BC| = 6.8\text{ cm}$ and the height $|AN| = 6\text{ cm}$ . Calculate the area of the trapezium.
(b)
The line $6y + kx - 12 = 0$ passes through the point $(-3, -4)$ . Find the value of $k$ .

Worked solution (try it first)

(a)

Drop perpendiculars from $A$ and $B$ to $DC$ , meeting it at $N$ and $M$ .
Both are the height, 6 cm.
In the right-angled triangle $ADN$ : $|DN| = \sqrt{7.5^2 - 6^2}$
$= \sqrt{20.25}$
$= 4.5$ cm.
In triangle $BMC$ : $|MC| = \sqrt{6.8^2 - 6^2}$
$= \sqrt{10.24}$
$= 3.2$ cm.
$NM = AB = 8$ cm, so $|DC| = 4.5 + 8 + 3.2 = 15.7$ cm.
Area $= \frac12(8 + 15.7) \times 6$
$= 71.1\text{ cm}^2$ .

(b)

The point lies on the line, so its coordinates satisfy the equation: $6(-4) + k(-3) - 12 = 0$ , so $-36 - 3k = 0$ and $k = -12$ .

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