WAEC Mathematics 2016 Paper

Concept:The trapezium is divided into three equal triangles by the lines $QN$ and $NP$.Explanation:Since $MQ \parallel NP$ and $QP \parallel MN$, quadrilateral $MQPN$ is a parallelogram.The diagonal $QN$ divides this parallelogram into two equal triangles.So, area of $\triangle QMN =$ area of $\triangle QNP$.Similarly, since $NQ \parallel OP$ and $QP \parallel NO$, quadrilateral $NOPQ$ is also a parallelogram.Thus, area of $\triangle PNO =$ area of $\triangle QNP$.Therefore, the trapezium $MOPQ$ contains three equal triangles: $\triangle QMN$, $\triangle QNP$, and $\triangle PNO$.Area of $\triangle QNP = \frac{1}{2} \times |QP| \times \text{height}$$= \frac{1}{2} \times 9 \times 6 = 27\text{ cm}^2$.So, area of trapezium $= 3 \times 27 = 81\text{ cm}^2$.Answer:Area of the trapezium is $81\text{ cm}^2$.Hence, the correct option is C.