In the diagram PS 9 cm OR 5cm P hat S R 63 o an... - WAEC Mathematics 2003 Question
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 option: a
Considering the triangle in the diagram
\(tan\theta = \frac{opp}{hyp}\
Tan 63^{\circ} = \frac{h}{4}\
h = 4 tan 63^{\circ}\
Area of trapezium = \frac{1}{2}h(a+b)\
\left(\frac{1}{2} \times 4 tan 63^{\circ}[5+9]\right)\
=28\times 1.963 = 54.96 = 55cm^2\)
\(tan\theta = \frac{opp}{hyp}\
Tan 63^{\circ} = \frac{h}{4}\
h = 4 tan 63^{\circ}\
Area of trapezium = \frac{1}{2}h(a+b)\
\left(\frac{1}{2} \times 4 tan 63^{\circ}[5+9]\right)\
=28\times 1.963 = 54.96 = 55cm^2\)
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