ABC is a right angled triangle, angle B=90* ,AB=28cm and BC=21cm With AC as diameter a semicircle is drawn - Maths - Areas Related to Circles

Question

ABC is a right angled triangle, angle B=90* ,AB=28cm and BC=21cm
With AC as diameter a semicircle is drawn and with BC as radius a
quarter cicle is drawn Find the area of the shaded region

Lalit Mehra · Accepted Answer

Area of the shaded region

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

In right ΔABC,

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 is 428.75 cm².

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ABC is a right angled triangle, angle B=90* ,AB=28cm and BC=21cm. With AC as diameter a semicircle is drawn and with BC as radius a quarter cicle is drawn. Find the area of the shaded region