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.

9-inch perimeter

A = sq. in.

Answer 1

An equilateral triangle has all sides congruent, denote them to be a inches. If the perimeter of this triangle is 9 inches, then

$P=3a=9\Rightarrow a=3\ \text{inches}.$

The area of the equialteral triangle is

$A=\dfrac{a^2\sqrt{3}}{4}=\dfrac{3^2\sqrt{3}}{4}=\dfrac{9\sqrt{3}}{4}\ \text{sq. in}.$

Answer: $\dfrac{9\sqrt{3}}{4}$ sq. in.