What is the area of the circle (approximately) inscribed in a triangle with side lengths 12 cm, 16 cm and 20 cm?

Explanation

The triangle is right-angled since 12^2 + 16^2 = 144 + 256 = 400 = 20^2. The inradius r of a right-angled triangle is given by \frac{a+b-c}{2} = \frac{12+16-20}{2} = 4 cm. The area of the inscribed circle is \pi r^2 = \pi (4)^2 = 16\pi \approx 16 \times 3.1416 \approx 50.26 square cm.

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