The perimeter of a triangle is 30 cm and the circumference of its incircle is 88 cm. The area of the triangle is

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We have to find the area of the given triangle. Perimeter of triangle is 30 cm. Let the radius of the circle be r. We have, Circumference of incircle=88 2pi r=88 r=14 Therefore, `ar (ΔABC)=ar (ΔOAB)+ar (ΔOBC)+ar(ΔOAC) = $\frac{1}{2}$ (r)(AB+BC+CA) = $\frac{1}{2}$ (14)(30) cm^2 = 210 cm^2` [Solution diagram: 63965_solution_1.png]

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