In the following figure, ABC is a right angled triangle in which ∠A = 90°, AB = 21 cm and AC = 28 cm. Semi-circles are described on AB, BC and AC as diameters. Find the area of the shaded region.
Answers
Answer:
The area of shaded region = 294 cm²
Step-by-step explanation:
Given :
ABC is a right angled triangle in which ∠A = 90°, AB = 21 cm and AC = 28 cm
In right angled ∆ABC,
BC² = AB² + AC²
BC² = 21² + 28²
BC² = 441 + 784
BC² = 1225
BC = √1225
BC = 35 cm
Diameter BC = 35 cm
Area of shaded region, A = Area of semicircle with AB as a diameter + Area of semicircle with AC as a diameter + Area of right angle ∆ ABC - Area of semicircle with BC as diameter
A = ½ π(21/2)² + ½ π(28/2)² + ½ × 21 × 28 - ½ π(35/2)²
[Area of semicircle = ½ πr² & Area of ∆ = ½ × base × height]
A = ½ π(21/2)² + ½ π(28/2)² - ½ π(35/2)² + ½ × 21 × 28
A = ½ π [10.5² + 14² - 17.5²] + 14 × 21
A = ½ π [110.25 + 196 - 306.25] × 294
A = ½ π [306.25 - 306.25] + 294
A = ½ π × 0 + 294
A = 0 + 294
A = 294 cm²
Area of shaded region = 294 cm²
Hence, the area of shaded region = 294 cm²
HOPE THIS ANSWER WILL HELP YOU….
Hi
Please see the attachment
And......
Please mark me as brainliest
