Question

Find the area of pentagon if AD = 5 cm, BC = 7 cm, AG = 5 cm and EF = 4 cm.

• A. 14 $c{m}^2$
• B. 22 $c{m}^2$
• C. 30 $c{m}^2$
• D. 44 $c{m}^2$

Answer 1

The correct option is D 44 $c{m}^2$

Area of pentagon =
Area of trapezium ABCD
+ Area of $△$BEC
= $\frac{1}{2}$$\times$(Sum of parallel sides)$\times$height
+ $\frac{1}{2}$$\times$base$\times$height
= $\frac{1}{2}$$\times$(AD+BC)$\times$AG
+ $\frac{1}{2}$$\times$BC$\times$EF
= $\frac{1}{2}$$\times$(5+7)$\times$5 + $\frac{1}{2}$$\times$7$\times$4
= $\frac{1}{2}$$\times$12$\times$5 + 7$\times$2
= 6$\times$5 + 7$\times$2
= 30 + 14 = 44 $c{m}^2$