The perimeter of a triangle is 24 cm and the circumference of its incircle is 88 cm. The area of the triangle is (taking = \(\pi \) = \(\frac{22}{7}\)):

168

Circumference of in-circle = 2\(\pi \)r = 88

⇒ 2 × \(\frac{22}{7}\) × r = 88

⇒ r = 14

⇒ Inradius = \(\frac{Area\;of\;triangle}{Semi\;perimeter\;of\;triangle}\)

ATQ

⇒ 14 = \(\frac{Area\;of\;triangle}{12}\)

Area of triangle = 14 × 12  =  168 cm²