Question

What is the area, rounded to the nearest tenth of square inch, of an equilateral triangle that has a perimeter of 24 inches?

Answer 1

Answer: 27.7 square inches.

Step-by-step explanation:

Let 'a' be the side of equilateral triangle.

Then the perimeter of the triangle = a+a+a=3a

Given: Perimeter of the equilateral triangle = 24 inches

$\\\Rightarrow3a=24\\\\\Rightarrow\ a=8\ inches$

We know that the area of a equilateral triangle is given by :-

$A=\dfrac{\sqrt{3} a^2}{4}\\\\\Rightarrow\ A=\dfrac{\sqrt{3} (8)^2}{4}\\\\\Rightarrow\ A=27.71281292\approx27.7\ in.^2$

Answer 2

Answer:

$27.712 inches^2$

Step-by-step explanation:

Perimeter of equilateral triangle = $3 \times side$

We are given that an equilateral triangle that has a perimeter of 24 inches

So,  $3 \times side=24$

$Side=\frac{24}{3}$

$Side=8$

Area of equilateral triangle = $\frac{\sqrt{3}}{4}a^2$

a is the side

So, Area of equilateral triangle = $\frac{\sqrt{3}}{4}(8)^2$

So, Area of equilateral triangle = $27.712 inches^2$

Hence the area of equilateral triangle is $27.712 inches^2$