Finding Equilateral Triangle Area from Perimeter

To find the area of an equilateral triangle given its perimeter, we first need to determine the length of one side.

Calculating Side Length

An equilateral triangle has three equal sides. The perimeter is the total length of all sides.

• Given Perimeter = 24 cm
• Perimeter of an equilateral triangle = 3 × side length (s)
• Therefore, 24 cm = 3 × s
• Solving for s: s = 24 cm / 3 = 8 cm

The side length of the equilateral triangle is 8 cm.

Calculating Triangle Area

The formula for the area of an equilateral triangle is:

Area = $\frac{\sqrt{3}}{4} \times s^2$

• Substitute the side length (s = 8 cm) into the formula:
• Area = $\frac{\sqrt{3}}{4} \times (8 \text{ cm})^2$
• Area = $\frac{\sqrt{3}}{4} \times 64 \text{ cm}^2$
• Area = $16\sqrt{3} \text{ cm}^2$

The area of the equilateral triangle is $16\sqrt{3} \text{ cm}^2$.