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The perimeter of a triangle is 10, and the area of the in-circle is $4\pi$. What is the area of the triangle?

I found the radius of the circle to be 2, but how can I use that to find the base and the height?

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Hint. The three segments from the in-center to the three vertices divide the triangle into three triangles.

Evaluate the sum of the areas of these three triangles.

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You can calculate the area with: $A=\frac{pr}{2}$, where $p$ is the perimeter of the triangle and $r$ the radius of the in-circle.

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