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,
Attached Figure / Diagram
A
55cm2
B
25cm2
C
22cm2
D
13cm2
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
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 = \(\frac{1}{2}h(a+b)\)
\(\frac{1}{2} \times 4 tan 63^{\circ}[5+9]\right)\)
= 28\(\times 1.963 = 54.96 = 55cm^2\)
Source: Myschool Past Questions Archive (Record #26612)