In the given figure, find the area of the shaded region and also its perimeter, if the lengths of AB - Maths - Areas Related to Circles

Question

In the given figure, find the area of the shaded region and also
its perimeter, if the lengths of AB and BC(in cm) is 28 and 21
respectively and BCD is a quadrant of a circle AEC is a semicircle
on AC as diameter ( Take Pie = 22/7)

Gursheen kaur. · Accepted Answer

Area of shaded region= Area of semi-circle with AC as diameter + Area of ΔABC – Area of quadrant of circle with BC as radius

In right ΔABC,

By Pythagoras theorem,

AC² = AB² + BC²

⇒AC² = (28 cm )² + (21 cm)²

⇒ AC² = 1225 cm²

⇒ AC = 35 cm

∴ Area of the shaded region,

$= \frac{1}{2} \times π (\frac{AC}{2})^{2} + \frac{1}{2} \times BC × AB - \frac{1}{4} \times π (BC)^{2} = \frac{1}{2} \times \frac{22}{7} \times (\frac{35 cm}{2})^{2} + \frac{1}{2} \times 21 cm × 28 cm - \frac{1}{4} \times \frac{22}{7} \times (21 cm)^{2} = 481.25 {cm}^{2} + 294 {cm}^{2} - 346.5 {cm}^{2} = 428.75 {cm}^{2}$

Thus, the area of the shaded region = 428.75 cm².

28

In the given figure, find the area of the shaded region and also its perimeter, if the lengths of AB and BC(in cm) is 28 and 21 respectively and BCD is a quadrant of a circle. AEC is a semicircle on AC as diameter ( Take Pie = 22/7)