In the diagram /PS/ = 9 cm, /OR/ = 5cm, \(P\hat{S}R = 63^o\) and \(S\hat{P}Q = P\hat{Q}R = 90^o\). Find, correct to the nearest whole number, the area of the trapezium,

In the diagram /PS/ = 9 cm, /OR/ = 5cm, \(P\hat{S}R = 63^o\) and \(S\hat{P}Q = P\hat{Q}R = 90^o\). Find, correct to the nearest whole number, the area of the trapezium,

A.

55cm2

B.

25cm2

C.

22cm2

D.

13cm2

Correct answer is A

Considering the triangle in the diagram
\(tan\theta = \frac{opp}{hyp}\\
Tan 63^{\circ} = \frac{h}{4}\\
h = 4 tan 63^{\circ}\\
Area of trapezium = \frac{1}{2}h(a+b)\\
\left(\frac{1}{2} \times 4 tan 63^{\circ}[5+9]\right)\\
=28\times 1.963 = 54.96 = 55cm^2\)