WAEC 2020 · Paper 1 · Q32

Plane mensuration

In the diagram, $PU \parallel SR$ , $PS \parallel TR$ , $QS \parallel UR$ , $|UR| = 15\text{ cm}$ , $|SR| = 8\text{ cm}$ , $|PS| = 10\text{ cm}$ and the area of triangle $SUR$ is $24\text{ cm}^2$ . Calculate the area of $PTRS$ .

The paper’s diagram is not drawn to scale; this redraw follows its layout.

Worked solution (try it first)

$\triangle SUR$ has base $SR = 8$ cm and its height is the distance between the parallel lines: $\frac12 \times 8 \times h = 24$ , so $h = 6$ cm.
$PT \parallel SR$ and $PS \parallel TR$ , so $PTRS$ is a parallelogram on base $SR$ with the same height.
Area $= 8 \times 6 = 48\text{ cm}^2$ , option B.

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