Question

finding the area of an equilateral triangle of known perimeter
what is the area, rounded to the nearest tenth of 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 triangle

Since the triangle is equilateral, all sides are equal. Divide the perimeter by 3:
$s = \frac{24}{3} = 8$ inches

Step2: Use area formula for equilateral triangle

The formula for the area of an equilateral triangle is $A = \frac{\sqrt{3}}{4}s^2$. Substitute $s=8$:
$A = \frac{\sqrt{3}}{4} \times 8^2$

Step3: Calculate the area

First compute $8^2=64$, then multiply by $\frac{\sqrt{3}}{4}$:
$A = \frac{\sqrt{3}}{4} \times 64 = 16\sqrt{3} \approx 16 \times 1.732 = 27.712$

Step4: Round to nearest tenth

Round 27.712 to one decimal place:
$A \approx 27.7$

Answer:

27.7 square inches