$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,

55cm²

25cm²

22cm²

13cm²

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Correct answer is A

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

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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,

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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,