JAMB 2004 · UME · Q27

Plane mensuration

In the diagram, $PQ = 4$ cm and $TS = 6$ cm; $PQTU$ and $PQRS$ are parallelograms. If the area of parallelogram $PQTU$ is $32\text{ cm}^2$ , find the area of the trapezium $PQRU$ .

Worked solution (try it first)

Area of parallelogram $PQTU$ is base × height, so the height is $32 \div 4 = 8$ cm.
Both parallelograms give $UT = PQ = 4$ cm and $SR = PQ = 4$ cm.
So $UR = 4 + 6 + 4 = 14$ cm.
Trapezium $PQRU$ : $\frac12(4 + 14) \times 8 = 72\text{ cm}^2$ , option D.

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