What is the area of an equilateral triangle with radius 15 centimeters? Round your answers to the nearest tenth, if necessary.

Radius is 2/3 of the height of an equilateral triangle.

15 = 2/3 h

h = 15 : 2/3 = 15 · 3/2 = 45/2 = 22.5 cm

a · cos 30° = h

a · √3/2 = h

a = 45/√3 = 15√3 cm

A = 1/2 · a · h = 1/2 · 15√3 · 22.5 = 0.5 · 15 · 1.7320508 · 22.5

A = 292.28 ≈ 292.3 cm²