If the radius of the circumscribed circle of a equalateral triangle is 10cm, what is the area?

Answer 1

Draw the radius from the center of the circle to the vertices of the triangle.

For each triangle, draw the height from the center of the circle to the side of the triangle.

There are 6 right triangles created, all of which have hypotenuse 10.

All 6 of these right triangles are congruent by Hypotenuse - Leg, since they

share perpendicular heights.

The equilateral triangle has 60 , 60, 60 degrees, so ALL 6 of the right triangles formed

are 30-60-90. Therefore, the legs of each of these right triangles are 5 and 5*Sqrt(3)

by the 30-60-90 proportionality rule.

So the total area is 75*Sqrt(3) and the area of the circle is pi*100