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

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) (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 =  = 82 square centimeters.

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