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,
-
55cm2
- 25cm2
- 22cm2
- 13cm2
The correct answer is: A
Explanation
\(tan\theta = \frac{opp}{hyp}\\
Tan 63^{\circ} = \frac{h}{4}\\
h = 4 tan 63^{\circ}\\
Area of trapezium = \frac{1}{2}h(a+b)\\
\left(\frac{1}{2} \times 4 tan 63^{\circ}[5+9]\right)\\
=28\times 1.963 = 54.96 = 55cm^2\)