Question

In the figure:- ABC is a right angle triangle, Angle B=90, Ab= 28cm and BC= 21 cm. With AC as diameter, a semicircle is drawn and with BC as radius, a quadrant is drawn. Find the shaded region. (Image attached below)
Genuine answers only. Do explain with proper steps...

Answer 1

*Question:-

In the figure:- ABC is a right angle triangle, Angle B=90, Ab= 28cm and BC= 21 cm. With AC as diameter, a semicircle is drawn and with BC as radius, a quadrant is drawn. Find the shaded region.

*Answer:-

In right ∆ABC, right angled at B

• AC² = AB²+BC² (By Pythagoras theorem)
• AC² = 28²+21²
• AC² = 784 + 441
• AC² = 1225
• AC = √1225
• AC = 35 cm

Area of Shaded Region = Area of ∆ABC + Area of semi-circle with diameter AC - Area of quadrant with radius BC.

$= > \frac{1}{2}(21 \times 28) + \frac{1}{2} \times \frac{22}{7} \times \frac{35}{2} \times \frac{35}{2} \\ \\ - \frac{1}{4} \times \frac{22}{7} \times 21 \times 21$

• 294 + 481.25 - 346.5
• 775.25 - 346.5
• 428.75 cm²

Hence the area of the Shaded Region is 428.75cm².