# 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 a octagon and its length is 5 cm. Calculate its area ?

**Solution:**

Given :

The polygon is octagon. Hence, n = 8.

Area of a regular polygon = $\frac{1}{2}$ n sin $\frac{360^o}{n}$ S^{2}

Where, *s* is the length from center to corner.

Area of a octagon = $\frac{1}{2}$ $\times$ sin $\frac{360^o}{8}$ 5^{2}

= 0.5 $\times$ sin $\frac{360^o}{8}$ 5^{2}

= 0.5 $\times$ 0.707 $\times$ 25

= 8.83 m^{2}.