Question

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

Answer 1

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