JAMB 1990 · UME · Q31

Plane mensuration

In a trapezium $PQRS$ with $QR \parallel PS$ , the area is $73.5\text{ cm}^2$ and the height is 10.5 cm. Find the length of $PS$ if $QR$ is one-third of $PS$ .

Worked solution (try it first)

Area of a trapezium $= \frac12(a + b)h$ .
Put in $QR = \frac13PS$ : $\frac12\left(PS + \frac13PS\right) \times 10.5 = 73.5$ .
Double both sides and divide by 10.5: $\frac43PS = 14$ .
Multiply by $\frac34$ : $PS = 10.5 = 10\frac12$ cm, option D.

Report a problem with this question