__Category__: Plane Geometry"Published in Newark, California, USA"

Find the area of an equilateral triangle inscribed in a circle with radius 2√3.

__Solution__:

To illustrate the problem, it is better to draw the figure as follows

Photo by Math Principles in Everyday Life |

If an equilateral triangle is inscribed in a circle, then the radius of a circle bisects the angles of an equilateral triangle. Each angle of an equilateral triangle is 60°. In this case if you analyze further the figure, there are six 30° - 60° right triangles. In this problem, we need the length of the base and the altitude of an equilateral triangle.

The base of an equilateral triangle is

The altitude of an equilateral triangle is

Therefore, the area of an equilateral triangle is

There's another way in getting the area of an equilateral triangle. If you know the sides of an equilateral triangle, then we can use the Heron's Formula as follows

The semi-perimeter of an equilateral triangle is

Therefore, the area of an equilateral triangle is