# Polygon Calculator

The term polygon originates from the Greek word poly - meaning “many” and “- gon,” meaning “angles.

## What is Polygon Calculator?

'**Polygon Calculator**' is an online tool that helps to calculate the area and perimeter of a polygon. Online Polygon Calculator helps you to calculate the area and perimeter of a polygon within a few seconds.

### Polygon Calculator

## How to Use Polygon Calculator?

Please follow the below steps to find the area and perimeter of a polygon:

**Step 1:**Enter the number of sides of a polygon and the length of the side in the given input box.**Step 2:**Click on the**"Calculate"**button to find the area and perimeter of a polygon.**Step 3:**Click on the**"Reset"**button to clear the fields and enter new values.

## How to Find Polygon Calculator?

A polygon is a closed two-dimensional figure, that comprises three or more straight lines.

The area of the polygon is defined as the amount of space enclosed within the boundary of an polygon. It is measured in square units.

**Area of the polygon = (s) ^{2} × N / 4tan(π / N)**

Where 's' is the length of the side of the polygon, 'N' is the number of sides of the polygon, and assume π is 180°

The perimeter of an N-sided polygon is defined as the sum of all the sides of the N polygon.

**The perimeter of an N-sided polygon = N × s**

Where 'N' is the number of sides of the polygon and 's' is the length of the side of the polygon, and assume π is 180°

**Solved Examples on Polygon Calculator**

**Example 1:**

Find the area and perimeter of a polygon if the number of sides of a polygon is 3 and the length of a side of the polygon is 5 units.

**Solution:**

Area of the polygon = (s)^{2} × N / 4tan(π / N)

= 5^{2} × 3 / 4tan(180 / 3) [assume π = 180°]

= 25 × 3 / 4tan60°

= 10.839 square units

Perimeter of a polygon = N × s

= 3 × 5

= 15 units

**Example 2:**

Find the area and perimeter of the polygon if the number of sides of a polygon is 5 and the length of a side of the polygon is 7 units.

**Solution:**

Given: Number of sides = 5 and length of side = 7 units

Area of the polygon = (s)^{2} × N / 4tan(π / N)

= 7^{2} × 5 / 4tan(180 / 5) [assume π = 180°]

= 49 × 5 / 4tan36°

= 84.48 square units

The perimeter of the polygon = sum of all sides of a polygon

= 7 + 7 + 7 + 7 + 7

= 35 units.

**Example 3:**

Find the area and perimeter of the polygon if the number of sides of a polygon is 4 and the length of a side of the polygon is 6 units.

**Solution:**

Given: Number of sides = 4 and length of side = 6 units

Area of the polygon = (s)^{2} × N / 4tan(π / N)

= 6^{2} × 4 / 4tan(180 / 4) [assume π = 180°]

= 36 × 4 / 4tan45°

= 36 square units

The perimeter of the polygon = sum of all sides of a polygon

= 6 + 6 + 6 + 6

= 24 units.

Similarly, you can try the calculator to find the area and perimeter of a polygon for the following:

- Number of sides = 7 and length of the side of the polygon = 14 units
- Number of sides = 9 and length of the side of the polygon = 8 units

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