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, a closed figure with many angles is called a polygon.

There are many properties in a polygon like sides, diagonals, area, angles, etc. Let’s 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 Example

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

Solution:

Given,

The polygon is an octagon.

Hence, n = 8.

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

Where s is the length from centre to corner.

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

= 4 × 0.707 × 25

= 70.72 sq.m.