Question

A circle has a radius of 6 in. The circumscribed equilateral triangle will have an area of

Answer 1

We need to find a and b. b is half the length of the triangle, a is part of the height (add the 6 to a, and we get the height). Then we can use Area = half base * height.

Answer 2

You should know that the angles of an equilateral triangle are 60 degrees. The 6in radius will bisect that angle (divide it in half) so the angle below is 30 degrees.


Now use sine and cosine (sine is opposite/hypotenuse, cos is adjacent/hypotenuse):
\[\large \sin 30 = \frac{ a }{ 6 }\] \[\large \cos 30 = \frac{ b }{ 6 }\]