We are given three sides of triangle and we want to find area of a circle inscribed in this given triangle. Lets take an example.
We are given the following triangle with sides equal to 50 cm, 35 cm and 40 cm. We want to find area of circle inscribed in this triangle.
The area of circle =
So, if we can find the radius of circle, we can find its area.
We have one relation among semi-perimeter of triangle and the radius of circle inscribed in such a triangle which is:
Area of triangle (1)
S – Semi-perimeter of triangle
r – radius of inscribed circle
We can find area of given triangle using Heron’s Formula.
Semi-Perimeter =
cm
Area of Triangle using Heron’s Formula =
Now, using formula number (1) to find the radius of circle:
= Area of Triangle
cm
Area of circle =
Rochelle Aguinaldo says
Hi. I just want to ask kindly explain the process of getting the radius on the inscribed circle? 🙂 because the formula that I used is different from you so i was a little bit confused. Thank you
Amos kimeli says
Nice