Question

Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Find the area of an equilateral triangle (regular 3-gon) with the given measurement.

3-inch radius

A = sq. in.

Answer 1

Answer: A =  (27/4)√3 in²

Explanation:

You are required to calculate the area, A, of an equilateral triangle, when you know its radius is 3 inches.

The radius of an equilateral triangle is the radius of the cirscumscribed circle.

The equilateral triangle has several characteristics which can be geometrically deduced:

• Three congruent sides (by definition)
• Three 60° internal angles
• If you call the length of the sides x, and the radius of the circumscribed circle r, then:

       r = x √3 / 3 ⇒ x = r√3

       Area = [√3 / 4] x²

• Combining the two previous relations, you deduce:

        Area = [3 √3 / 4] r²

By substituting the given radius, you find the area of the equilateral triangle:

            Area = [3 √3 / 4] x² = [3 √3 / 4] (3 in)² = 27√3 / 4 in²