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 $c{m}^2$
• B. 60 $c{m}^2$
• C. 75.2 $c{m}^2$
• D. 93.6 $c{m}^2$

Answer 1

The correct option is D 93.6 $c{m}^2$

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
= $\frac{1}{2}$$\times$(Sum of parallel sides)$\times$height

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

= $\frac{1}{2}$$\times$(AD+FE)$\times$OQ + $\frac{1}{2}$$\times$(AD+BC)$\times$OP
= $\frac{1}{2}$$\times$(12+6)$\times$5.2+ $\frac{1}{2}$$\times$(12+6)$\times$5.2
= $\frac{1}{2}$$\times$18$\times$5.2+ $\frac{1}{2}$$\times$18$\times$5.2
= 9$\times$5.2+ 9$\times$5.2 = 46.8+46.8 = 93.6 $c{m}^2$