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.
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Answered by
106
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
= 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
Answered by
25
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
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