Question

What is the area of the pentagon using either of the approaches?

• A. $50{\text{cm}}^2$
• B. $80{\text{cm}}^2$
• C. $100{\text{cm}}^2$
• D. $160{\text{cm}}^2$

Answer 1

The correct option is C $100{\text{cm}}^2$

(1)
Area of pentagon = Area of trapezium ABCF + Area of trapezium AFDE
As both trapeziums are congruent,
Area of pentagon = 2$\times$area of trapezium ABCF
=2$\times$$\frac{1}{2}$$\times$(sum of parallel sides)$\times$height
= 2$\times$$\frac{1}{2}$$\times$(BC+AF)$\times$CF
= (BC+AF)$\times$CF
= (10+15)$\times$4 = 100 ${\text{cm}}^2$

OR
(2)
Area of pentagon = Area of $△$ABE
+ Area of rectangle BCDE

Area of $△$ABE = $\frac{1}{2}$$\times$base$\times$height
= $\frac{1}{2}$$\times$BE$\times$AF = $\frac{1}{2}$$\times$8$\times$5 = 4$\times$5 = 20 ${\text{cm}}^2$

Area of rectangle BCDE
= length$\times$breadth
= BC$\times$CD = 10$\times$8 = 80 ${\text{cm}}^2$
Area of pentagon = 20+80 = 100 ${\text{cm}}^2$