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Question

A restaurant POQR is being constructed in the middle of a circular lake. The circle, which has its center at O is touching the mid-points of the boundary ABCD as shown in the figure. AB=CD and AD=BC. If BC=8 cm, then the area of AQOP is


A

14× Area of ABCD

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B

12× Area of ABCD

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C

18× Area of ABCD

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D

None of these

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Solution

The correct option is A

14× Area of ABCD


Given, BC = 8 cm
AB=8 cm[AB=BC]
Now, AP=12AB=4 cm
Area of AQOP = 4×4=16 cm2
and area of ABCD= 8×8= 64 cm2
Area of AQOPArea of ABCD=1664=14
Area of AQOP=14×Area of ABCD


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