# Polygon Formula

Polygon is a word derived from The Greek language, where poly means many and gonna means angle. So we can say that in a plane, closed figure with many angles is called a polygon. The given diagram is how a polygon looks like:

There are many properties in a polygon like sides, diagonals, area, angles, etc. Lets know how to find using these polygon formulae.

Polygon formula to find area:

$\large Area\;of\;a\;regular\;polygon=\frac{1}{2}n\; sin\left(\frac{360^{\circ}}{n}\right)s^{2}$

Polygon formula to find interior angles:

$\large Interior\;angle\;of\;a\;regular\;polygon=\left(n-2\right)180^{\circ}$

Polygon formula to find the triangles:

$\large Interior\;of\;triangles\;in\;a\;polygon=\left(n-2\right)$

Where, n is the number of sides and S is the length from center to corner.

### Solved Examples

Question: A polygon is an octagon and length from centre to its vertex is 5 cm. Calculate its area.

Solution:

Given :

The polygon is octagon. Hence, n = 8.

Area of a regular polygon = 1/2 × n × (sin 360°/n) × S2

Where, s is the length from center to corner.

Area of a octagon = 1/2 × 8 × (sin 360°/8) × 52

= 4 × 0.707 × 25

= 70.72 sq.m.