Question

the area of a regular polygon is 36 inches squared. find the length of a side if the polygon is a triangle

Answer 1

Answer on Question #40080 – Math - Geometry

the area of a regular polygon is 36 inches squared. Find the length of a side if the polygon is a triangle

Solution

By regular triangle we mean an equilateral triangle.

Denote

$\mathbf{a} =$ length of a side,

$$\mathbf{Area} = \frac{\alpha^2 \sqrt{3}}{4}.$$

Then $\alpha = \sqrt{\frac{4 + \mathbf{Area}}{\sqrt{3}}} = \sqrt{\frac{4 + 36}{\sqrt{3}}} \approx 9.12$ (in)

Answer: $\alpha = \sqrt{\frac{4 + \mathbf{Area}}{\sqrt{3}}} \approx 9.12$ (in)