Question

Find the area of the shaded region

Answer 1

Area of the shades region = 244.6 ft²

Explanation:

Area of the shaded region = Area of the rectangle ABCD- Area of the right angle triangle DEC

Area of the rectangle = Length × width

= 29.8 × 13

= 387.4 ft²

By applying Pythagoras theorem in the right triangle DEC,

(Hypotenuse)² = (leg 1)² + (leg 2)²

CD² = DE² + EC²

(29.8)² = DE² + (28)²

888.04 = DE² + 784

DE² = 888.04 - 784

DE = 10.2 ft

Area of ΔDEC =
`(1)/(2)(\text{Base})(\text{Height})`

=
`(1)/(2)(10.2)(28)`

= 142.8 ft²

Area of the shades region = 387.4 - 142.8

= 244.6 ft²