Question

Find the area of each regular polygon. Round to the nearest tenth.

Answer 1

Given:

A regular polygon with three vertices and side 14 cm.

To find:

Area of the regular polygon.

Solution:

We know that, a regular polygon has equal sides and equal interior angles.

The given regular polygon has three equal sides, it means it is an equilateral triangle.

The area of an equilateral triangle is:

$A=\dfrac{\sqrt{3}}{4}a^2$

Where, a is the side length of the triangle.

Putting $a=14$, we get

$A=\dfrac{\sqrt{3}}{4}(14)^2$

$A=\dfrac{\sqrt{3}}{4}(196)$

$A=84.87049$

$A\approx 84.9$

Therefore, the area of given regular polygon is 84.9 cm².