Question: An archaeologist discovers a triangular stone tablet with a right angle. The hypotenuse measures $ 13 $ cm, and the radius of the inscribed circle is $ 2 $ cm. What is the area of the triangle?

March 11, 2026

Question: An archaeologist discovers a triangular stone tablet with a right angle. The hypotenuse measures $ 13 $ cm, and the radius of the inscribed circle is $ 2 $ cm. What is the area of the triangle?

**An archaeologist discovers a triangular stone tablet with a right angle. The hyp

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So, the area of the triangle can also be expressed as:
Now, recall that in a right triangle, the inradius is given by:
Therefore, the ratio of the area of the circle to the area of the triangle is:
Using the formula for the inradius of a right triangle:
Question: A mammalogist observes that the cross-section of a whales tail is a circle inscribed in a right triangle with legs of lengths $ a $ and $ b $. If the hypotenuse is $ 10 $ cm and the inradius is $ 2 $ cm, find the area of the triangle.
Using the formula for area in terms of the inradius and semiperimeter:

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