Question

What is the area of an equilateral triangle with a side length of $ 5? $

Answer 1

Hint: Equilateral triangles are the triangle having all the three sides and all three angles equal. Area of an equilateral triangle can be expressed by $ \dfrac{{\sqrt 3 }}{4}{a^2} $ where “a” is the measure of the side of the triangle. Area of the hexagon is equal to six times the area of an equilateral triangle. Also, by substituting the value of the side in the formula, will find the area of the triangle.

Complete step-by-step answer:
Side of the triangle $ a = 5 $ units
Now, the area of the triangle is $ A = \dfrac{{\sqrt 3 }}{4}{a^2} $
Place the value of “a” in the above expression –
 $ A = \dfrac{{\sqrt 3 }}{4}{(5)^2} $
Simplify the above equation –
 $ A = \dfrac{{25\sqrt 3 }}{4} $ square units
So, the correct answer is “ $ A = \dfrac{{25\sqrt 3 }}{4} $ square units”.

Note: Area can be calculated using the Heron’s formula. Heron’s formula was created by Heron of Alexandria. It is also known as Heron's formula. This formula is most widely used where all the sides of the triangle are known and without knowing its angles. First here we will find the perimeter of the triangle and then its area by using Heron’s formula - $ A = \sqrt {s(s - a)(s - b)(s - c)} $