Question

Find the area of a circle circumscribed about an equilateral triangle whose side is 18 inches long.

a. 81
b. 108
c. 243

Answer 1

circumradius of equilateral triangle =
a over 3√

where a = side of the triangle

Answer 2

area of the circle = pi * square(circumradius)

Answer 3

L = R√3 ==> so R = L/√3

Area of the circle is πR² = πL²/3 = 108π in²

Answer 4

So, B.

Answer 5

Did this help?

Answer 6

Doesnt make sense. But thank you.

Answer 7

Anyways, if the triangle is equilateral, and the circle is circumscribed, the circle is outside of the triangle.

To find the area, you need the radius.

The radius should be a straight line from the center of the triangle to any of it's points.

Draw lines from the center of the circle to each of the triangle points.

Draw three more lines from the center to the middle of the sides of the triangle.

You should now have six separate 30-60-90 triangles inside of your original triangle. Use your 30-60-90 rules to solve for the radius, then the circumference.

This is called "Bisecting"