Question

if the inradius of an equilateral triangle is 12cm then the area of triangle is ​

Answer 1

Given,

Inradius of the given equilateral triangle is 12 centimetres.

For calculating,the area of the given equilateral triangle,we have to calculate the length of the side of the given equilateral triangle.

Let,the side = x centimetres (assume x as a variable to perform the further mathematical calculations)

Inradius = x/2√3 centimetres

Now, comparing the value of the length of inradius of the given equilateral triangle that we have calculated and the value of the length of the inradius of the given equilateral triangle that is given in the question,we will get the following mathematical equations.

x/2✓3 = 12

x = 24✓3

So, area = ✓3/4 × (24✓3)² = (√3 × 24 × 24 × 3)/4 = ✓3 × 6 × 24 × 3 = 432✓3 cm²

Hence,the area of the given equilateral triangle is 432✓3 cm².