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Regular Polygon Area Calculator

The area of a regular polygon is the measure of the space enclosed within its boundaries. A regular polygon is a shape with equal sides and angles. Calculating its area involves specific formulas based on the number of sides it possesses.

How to Use the Calculator ?

Enter the number of sides (n) of the regular polygon.

Enter the length of each side (s) of the regular polygon.

Click on the 'Calculate' button to instantly find the area of the regular polygon.

When should I use this calculator ?

This calculator is helpful whenever you need to quickly determine the area of a regular polygon without going through extensive manual calculations.

What is the formula for the area of a regular polygon?

The formula for finding the area of a regular polygon is:

Area=n×s2×cot(π/n)4

Where:

n = number of sides

s = length of each side

π = Pi (approximately 3.14159)

Can the calculator find the area for irregular polygons?

No, this calculator is specifically designed for regular polygons with equal sides and angles.

Is there a limit to the number of sides this calculator can handle?

The calculator can compute the area for regular polygons with up to 10 sides, including the option for n sides.

Examples:

Example 1:

Let's find the area of a regular pentagon (5 sides) with each side measuring 6 units.

Solution:

Number of sides (n) = 5

Length of each side (s)= 6 units

Using the formula:

Area=5×62×cot(π/5)4

Area = 647.373. units

Example 2:

Consider a regular hexagon (6 sides) with a side length of 8 units.

Solution:

Number of sides (n) = 6

Length of each side (s)= 8 units

Using the formula:

Area=6×82×cot(π/6)4

Area = 4661.6656. units


Other polygons include pentagon, hexagon, heptagon, and so on as given the table below.
Polygon(s)NameNumber of Sides
3-sidedTriangle3
4-sidedSquare4
5-sidedPentagon5
6-sidedHexagon6
7-sidedHeptagon7
8-sidedOctagon8
9-sidedNonagon9
10-sidedDecagon10
n-sidedn-gonn

FAQs

What's the difference between a regular and irregular polygon?
Why is it important to know the area of a regular polygon?
How do you derive the formula for the area of a regular polygon?
Why does the formula include the tangent function?

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