The diagram, MOPQ is a trapezium with QP||MO, MQ||NP, NQ||OP, |QP| = 9cm and the...

WAEC 2016

The diagram, MOPQ is a trapezium with QP||MO, MQ||NP, NQ||OP, |QP| = 9cm and the height of \(\Delta\) QNP = 6cm, calculate the area of the trapezium.

A. 96cm²
B. 90cm²
C. 81cm²
D. 27cm²

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Correct Answer: Option C

Explanation

Area of \(\Delta\) QNP = \(\frac{1}{2} \times 9 \times 6 \) = 27cm²

Area of \(\Delta\) QMN = Area of \(\Delta\) QNP

= Area of \(\Delta\) PNO (triangles between the same parallels)

Hence, area of the trapezium

3 x area of \(\Delta\) QNP

= 3 x 27

= 81cm²

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