Find the area of an equilateral triangle (regular 3-gon) with the given measurement. 6-inch side. a = sq. in.

We need a base and a height to find the area.

The base is one of the sides of the equilateral triangle and measures 6 inches.

Use any side as the base.

Now we need the height.

Draw the altitude to the base. This altitude is the height we need. We need its length.

Now you have 2 right triangles that are 30-60-90 triangles.

Half of the side that is bisected by the altitude is a short leg of the right triangle.

The altitude of the equilateral triangle is the long leg of the right triangle.

In a 30-60-90 triangle,

short leg = (1/2) * hypotenuse

long leg = sqrt(3) * short leg

The short leg measures (1/6) * hypotenuse = (1/2) * 6 inches = 3 inches

The long leg measures sqrt(3) * short leg = 3sqrt(3) inches

The long leg is the altitude which is the height.

area of triangle = bh/2 = (6 inches)(3 * sqrt(3) inches)/2 = 9sqrt(3) in^2