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In the given figure, 3 semicircles are drawn on three sides of triangle ABC. AB = 21 cm, BC = 28 cm and AC = 35 cm. What is the area (in cm2) of the shaded part?

In the given figure, 3 semicircles are drawn on three sides of triangle ABC. AB = 21 cm, BC = 28 cm and AC = 35 cm. What is the area (in cm2) of the shaded part? Correct Answer 294

ABC is a right angled triangle, because the sides are Pythagorean triplet

⇒ Area of triangle ABC = (1/2) × 21 × 28 = 294

⇒ Area of semicircle with diameter AB = (22/14) × (21/2) × (21/2) = 693/4

⇒ Area of semicircle with diameter BC = (22/14) × (28/2) × (28/2) = 308

⇒ Area of semicircle with diameter AC = (22/14) × (35/2) × (35/2) = 1925/4

⇒ Area of shaded region = Area of triangle ABC + Area of semicircle AB + Area of semicircle BC - Area of semicircle AC

⇒ Area of shaded region = 294 + (693/4) + 308 - (1925/4) = 294

∴ Required Area is 294 cm2

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