Question

What is the area of an equilateral triangle with sides 8 inches long?

Answer 1

Hint: To find the area of an equilateral triangle with sides 8 inches long, we have to use the formula $A=\dfrac{\sqrt{3}}{4}{{a}^{2}}$ , where a is the side of an equilateral triangle. We know that an equilateral triangle will have all the three sides of the same length. Therefore, here $a=8\text{ inch}$ .

Complete step-by-step answer:
We have to find the area of an equilateral triangle with sides 8 inches long. Let us first recollect what an equilateral triangle is. An equilateral triangle will have all the three sides of same length and all the angles will be equal to $60{}^\circ $ .

We know that area of an equilateral triangle is given by
$A=\dfrac{\sqrt{3}}{4}{{a}^{2}}$
where a is the side of an equilateral triangle. Here, we are given that $a=8\text{ inch}$ . Therefore, the required area can be found as follows.
$\Rightarrow A=\dfrac{\sqrt{3}}{4}{{8}^{2}}$
Let us take the square of 8.
$\Rightarrow A=\dfrac{\sqrt{3}}{4}\times 64$
We can cancel the common factor 4 from 64 and the denominator.
$\begin{align}
  & \Rightarrow A=\dfrac{\sqrt{3}}{\require{cancel}\cancel{4}}\times {{\require{cancel}\cancel{64}}^{16}} \\
 & \Rightarrow A=16\sqrt{3}\text{ i}{{\text{n}}^{2}} \\
\end{align}$
Hence, the area of an equilateral triangle with sides 8 inches long is $16\sqrt{3}\text{ i}{{\text{n}}^{2}}$ .

Note: Students must know the formula of area of an equilateral triangle. They may assume that the area of the equilateral triangle is the same as that of a triangle. Area of a triangle is given as $A=\dfrac{1}{2}\times \text{base}\times \text{height}$ . They may also get confused with the area and perimeter of the equilateral triangle. The latter is given as $P=3a$ .