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Question

In given regular hexagon, if AD = 10 cm, AB = 5 cm and FB = 8.66 cm, find area of hexagon.

A
32.49 cm2
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B
64.95 cm2
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C
97.43 cm2
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D
129.9 cm2
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Solution

The correct option is B 64.95 cm2
Given: In regular hexagon all sides are equal
AB=BC=CD=DE=EF=FA = 5 cm
FO = BO = 12×FB = 12×8.66 = 4.33 cm

Area of hexagon
= Area of trapezium ADEF
+ Area of trapezium ADCB

Area of hexagon
= 12×(AD+EF)×FO + 12×(AD+BC)×BO
=12×(AD+EF)×FO + 12×(AD+EF)×FO
........( EF=BC and FO=BO)
= (AD+EF)×FO
= (AD+EF)×FB2
= (10+5)×8.662
= (15)×8.662= 15×4.33 = 64.95 cm2


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