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Question

In given hexagon, length of all sides equals to 6 cm, then find its area if AD = 12 cm, and PO = OQ = 5.2 cm.

A
45 cm2
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B
60 cm2
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C
75.2 cm2
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D
93.6 cm2
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Solution

The correct option is D 93.6 cm2
Given: Area of above hexagon can be broken down into area of 2 trapeziums namely ADFE and ADCB
AB=BC=CD=DF=FE=AE.

We know,
Area of trapezium
= 12×(Sum of parallel sides)×height

Area of hexagon
= Area of trapezium ADFE
+ Area of trapezium ADCB

= 12×(AD+FE)×OQ + 12×(AD+BC)×OP
= 12×(12+6)×5.2+ 12×(12+6)×5.2
= 12×18×5.2+ 12×18×5.2
= 9×5.2+ 9×5.2 = 46.8+46.8 = 93.6 cm2

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