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Question

# The area of the trapezium PQRS is approximately:

A
8.4 cm2
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B
5.75 cm2
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C
5.25 cm2
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D
4.2 cm2
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Solution

## The correct option is B 4.2 cm2According to the property of trapezium, PQ must be parallel to RS.So, AS = RBPSsin60=QRsin30PS=2.3×sin30sin60PS=1.3From the figure, it is clear that,RS = PQ-(PA+QB)RS=PQ−(PScos60+QRcos30)RS=5−(1.3cos60+2.3cos30)RS=2.3In the trapezium PQRS,SA=PSsin60SA=1.3sin60SA=1.1Now, area of trapezium PQRS=12×(Sumoflengthofparallelsides)×height=12×(2.3+5)×1.1=4.2So, correct answer is option D.

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