Question

In rectangle ABCD, DE and BF are 2 cm and 5 cm respectively. If AB and BC are 12 cm and 10 cm respectively, then find area of shaded region

• A. 10 $c{m}^2$
• B. 30 $c{m}^2$
• C. 80 $c{m}^2$
• D. 120$c{m}^2$

Answer 1

The correct option is C 80 $c{m}^2$

Given : ABCD is a rectangle
AB = 12 cm, BC = 10 cm
DE = 2 cm, BF = 5 cm

Area of rectangle = length$\times$breadth
Area of rectangle ABCD = AB$\times$BC
= 12$\times$10 = 120 cm${}^2$

Area of triangle = $\frac{1}{2}$$\times$base$\times$height
Area of $△$ABF = $\frac{1}{2}$$\times$AB$\times$BF
= $\frac{1}{2}$$\times$12$\times$5 = 6$\times$5 = 30 cm${}^2$

Area of $△$ADE = $\frac{1}{2}$$\times$DE$\times$AD
= $\frac{1}{2}$$\times$10$\times$2 = 5$\times$2 = 10 cm${}^2$

Area of shaded region = area of rectangle ABCD - Area of $△$ABF - Area of $△$ADE
= 120 - 30 - 10 = 80 cm${}^2$