In the diagram /PS/ = 9 cm, /OR/ = 5cm, (Phat{S}R = 63^o) and (Shat{P}Q…

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

Correct Answer: Option A

Explanation

Considering the triangle in the diagram
(tantheta = 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)\
=28times 1.963 = 54.96 = 55cm^2)