How To Calculate The Area Of A Circle Inside A Triangle Where The Length Of Three Sides Of The Triangle Are Given?

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Oddman answered
As with any circle, the area is given by
area = Pi*r2

The radius of an inscribed circle in a triangle with side lengths a, b, and c is
r = √((s-a)(s-b)(s-c)/s)
s = (a+b+c)/2.

This means the area can be calculated by
area = Pi*(s-a)(s-b)(s-c)/s
thanked the writer.
Anonymous commented
Many thanks for the solution. I looks correct--I did a to-scale drawing. But how did you derive the fomula. Your solution seems to be based on Heron's formula, but I don't know how you got from the area of the triangle to the area of the circle inside the triangle. Can you enlighten?

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