Question

What is the area of the equilateral triangle having the length of the side 16cm?

Answer 1

Hint: We have given the side of the equilateral triangle. The equilateral triangle is defined as a triangle with all sides equal \[s = \dfrac{{a + b + c}}{2}\]and in this question the length of side is 8cm. We will utilize the area of an equilateral triangle formula, which is:
\[{\text{Area(A)}} = \dfrac{{\sqrt 3 }}{4}{a^2}\]
Where, A is the area of the triangle and a is the side.

Complete answer:
We are given the side of an equilateral triangle and we have to calculate its area. We must first understand what an equilateral triangle is. It is the triangle with all three sides equal in length, which is expressed as 8cm in this case.

(self-made)
We have all side equal to 16cm and we know that the formula for calculating the area of an equilateral triangle is
\[{\text{Area(A)}} = \dfrac{{\sqrt 3 }}{4}{a^2}\]
Here a is the length of each side and A is the area.
We will substitute the value of a in the above formula.
\[ \Rightarrow {\text{Area(A)}} = \dfrac{{\sqrt 3 }}{4}{a^2}\]
\[ \Rightarrow {\text{Area(A)}} = \dfrac{{\sqrt 3 }}{4}{16^2}\]
\[ \Rightarrow {\text{Area(A)}} = \dfrac{{\sqrt 3 }}{4}256\]
\[ \Rightarrow {\text{Area(A)}} = 64\sqrt 3 \]
So, we get the value of the area as \[64\sqrt 3 \] , and its units will be as follows: Since we used the square of the side in the calculation, the unit of area will be the square of the unit of the side, which is given as
Hence, the area of equilateral triangle having side 16cm is \[{\text{A}} = 64\sqrt 3 c{m^2}\]

Note: This formula for area is only true when all three sides of the triangle are equal, which implies it is only valid for the equilateral triangle. If we have a triangle with unequal sides, we may apply Heron's formula, which is as follows:
\[{\text{A}} = \sqrt {s(s - a)(s - b)(s - c)} \]
Here s stands for the triangle's semiperimeter, which is half of the entire perimeter, and a,b,c are the triangle's three sides.
So, \[s = \dfrac{{a + b + c}}{2}\]