# In the given figure, 3 semicircles are drawn on three sides f trian

^{2}) of the shaded part?

A. 588

B. 324

C. 294

D. 286

### Right Answer is: C

#### SOLUTION

Shaded area = [area of Δ + area of semicircle on AB + Area of semicircle on BC] – Area of Semicircle on AC

Area of triangle :

Since 21, 28 and 35 is a pythagorean triplet of (3,4,5) family

Thus area of triangle = 1/2 × 21 × 28 = 294

Area of s.c. AB = πr^{2}/2 = 693

Area of s.c. BC = 1232

Area of s.c. on AC = 1925

Thus required area = [294 + 693 + 1232] – 1925 = 294 cm^{2}

OR

**Short Trick:**

Shaded area = [area of Δ + area of semicircle on AB + Area of semicircle on BC] – Area of Semicircle on AC

= area of Δ + πAB^{2}/2 + πBC^{2}/2 – πAC^{2}/2 = area of Δ + π/2[AB^{2} + BC^{2} – AC^{2}]

= Area of triangle [Since AB^{2} + BC^{2} = AC^{2 }pythagorean triplet]

In the given figure, 3 semicircles are drawn on three sides f trian