Question

area and perimeter of triangles. what is the area of an equilateral triangle that has a perimeter of 36 centimeters? round to the nearest square centimeter. 72 square centimeters. 15 square centimeters. 62 square centimeters.

Explanation:

Step1: Find side - length of equilateral triangle

Since perimeter of equilateral triangle $P = 3s$ (where $s$ is side - length) and $P = 36$ cm, then $s=\frac{P}{3}=\frac{36}{3}=12$ cm.

Step2: Use area formula for equilateral triangle

The area formula for an equilateral triangle is $A=\frac{\sqrt{3}}{4}s^{2}$. Substitute $s = 12$ cm into the formula: $A=\frac{\sqrt{3}}{4}\times12^{2}=\frac{\sqrt{3}}{4}\times144 = 36\sqrt{3}\approx36\times1.732 = 62.352\approx62$ square centimeters.

Answer:

62 square centimeters