Question

area and perimeter of triangles
finding the area of an equilateral triangle of known perimeter
what is the area, rounded to the nearest tenth of a square inch, of an equilateral triangle that has a perimeter of 24 inches?
area = square inches
perimeter = 24 in.

Explanation:

Step1: Find side - length of equilateral triangle

Since perimeter $P = 3s$ (where $s$ is side - length) and $P = 24$ inches, then $s=\frac{P}{3}=\frac{24}{3}=8$ inches.

Step2: Use area formula for equilateral triangle

The area formula for an equilateral triangle is $A=\frac{\sqrt{3}}{4}s^{2}$. Substitute $s = 8$ into the formula: $A=\frac{\sqrt{3}}{4}\times8^{2}=\frac{\sqrt{3}}{4}\times64 = 16\sqrt{3}\approx16\times1.732 = 27.712$.

Step3: Round to the nearest tenth

Rounding $27.712$ to the nearest tenth gives $27.7$.

Answer:

$27.7$