SOLUTION: In the figure, P is the incenter of triangle ABC, the radius of the inscribed circle is 4cm, and the perimeter of triangle ABC is 41cm. What is the area of triangle ABC? Diagram

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Question 1149673: In the figure, P is the incenter of triangle ABC, the radius of the inscribed circle is 4cm, and the perimeter of triangle ABC is 41cm. What is the area of triangle ABC?
Diagram: https://imgur.com/BaacLUE
Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
.

For any triangle, its area is half the product the perimeter and the radius of the inscribed circle.


See the lesson

    - Proof of the formula for the area of a triangle via the radius of the inscribed circle  

in this site.


In your case, the area of the triangle ABC is


    area = %281%2F2%29%2A41%2A4 = 82 square centimeters.