Question

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

• A. 32.49 $c{m}^2$
• B. 64.95 $c{m}^2$
• C. 97.43 $c{m}^2$
• D. 129.9 $c{m}^2$

Answer 1

The correct option is B 64.95 $c{m}^2$

Given: In regular hexagon all sides are equal
AB=BC=CD=DE=EF=FA = 5 cm
FO = BO = $\frac{1}{2}$$\times$FB = $\frac{1}{2}$$\times$8.66 = 4.33 cm

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

Area of hexagon
= $\frac{1}{2}$$\times$(AD+EF)$\times$FO + $\frac{1}{2}$$\times$(AD+BC)$\times$BO
=$\frac{1}{2}$$\times$(AD+EF)$\times$FO + $\frac{1}{2}$$\times$(AD+EF)$\times$FO
........($\because$ EF=BC and FO=BO)
= (AD+EF)$\times$FO
= (AD+EF)$\times$$\frac{FB}{2}$
= (10+5)$\times$$\frac{8.66}{2}$
= (15)$\times$$\frac{8.66}{2}$= 15$\times$4.33 = 64.95 $c{m}^2$