Question

A circle with radius 4 inches is inscribed in an equilateral triangle. Find the area of the triangle.

Answer 1

The inscribed circle has its center at the point of intersection of the angle bisectors, which also happen to be the medians. Hence the altitude of the triangle is 3 times the radius, or 12 inches.

The side length of this triangle is 2/√3 times the altitude, so the area is

... Area = (1/2)·b·h = (1/2)·(24/√3 in)·(12 in)

... Area = 48√3 in² ≈ 83.1384 in²