JAMB 1991 · UME · Q44

In the figure, $PQRS$ is a square of side 8 cm; $UQ = 4$ cm, $QV = 6$ cm and $WR = 2$ cm. What is the area of $\triangle UVW$ ?

Worked solution (try it first)

Find the pieces of the square outside $\triangle UVW$ .
$\triangle UQV$ : $\frac12 \times 4 \times 6 = 12\text{ cm}^2$ .
$\triangle VRW$ has $VR = 8 - 6 = 2$ : $\frac12 \times 2 \times 2 = 2\text{ cm}^2$ .
$PUWS$ is a trapezium with parallel sides $PU = 4$ and $SW = 8 - 2 = 6$ , and height 8: $\frac12(4 + 6) \times 8 = 40\text{ cm}^2$ .
Take them from the square: $64 - (12 + 2 + 40) = 64 - 54$
$= 10\text{ cm}^2$ , option D.