Question

ABC is a right triangle with AB = 8 cm, BC = 6 cm and ∠B = 90°. A sector with B as centre and radius = 4 cm is cut as shown in the figure. Find the area of shaded portion.

Answer 1

Area of the shaded portion = 11.43 sq. cm.

Explanation:

Area of triangle ABC = 1/2 * base * height.

= 1/ 2 * BC * AB

= 1/ 2 * 6 * 8

= 24 sq. cm.

Area of the 1/ 4 circle portion = 1 / 4 * pi * radius^2

= 1/ 4 * 22 / 7 * 4 * 4  

= 88 / 7  

= 12.57 sq.cm.

Area of the shaded portion = Area of triangle ABC - area of the 1/ 4 circle portion

= 24 - 12.57

= 11.43 sq. cm.