Question

In figure ABC is a right angle triangle,angle B=90,AB=28cm and BC=21cm. With AC as diameter a semicircle is drawn and BC as radius a quarter circle is drawn. Find the area of the shaded region.
Pls write it in piece of paper and post it.

Answer 1

The area of the shaded region

= Area of Semi-circle + Area of triangle ABC - Area of quarter circle

Area of triangle = 1/2 x 21 x 28 = 294 cm²

To find area of semi-circle;

AC² = 28² + 21²
        = 1225

AC = 35

Radius of semi-circle = 35/2 = 17.5

Area = 1/2 x 3.14 x (17.5)² = 480.8 cm²

Area of quarter circle = 1/4 x 3.14 x 21²= 346.2 cm²

Area of shaded region = 294 + 480.8 - 346.2 = 428.6 cm²

Answer 2

The area of the shaded region

= Area of Semi-circle + Area of triangle ABC - Area of quarter circle

Area of triangle = 1/2 x 21 x 28 = 294 cm²

To find area of semi-circle;

AC² = 28² + 21²

       = 1225

AC = 35

Radius of semi-circle = 35/2 = 17.5

Area = 1/2 x 3.14 x (17.5)² = 480.8 cm²

Area of quarter circle = 1/4 x 3.14 x 21²= 346.2 cm²

Area of shaded region = 294 + 480.8 - 346.2 = 428.6 cm²