Area of a Polygon Calculator

Last updated: 10 Nov 2025 | Author: Brij | Review By: Irshad

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Calculate the area of any regular or irregular polygon instantly using our Area of a Polygon Calculator. Includes formulas, and step-by-step solved examples.

Polygon Type:

Number of Sides:

sides

Length of Each Side:

Apothem (optional):

Polygon Calculation Results

Area of Polygon:

sq ft

Perimeter of Polygon:

When working with construction, design, geometry, or land measurement, calculating the area of a polygon is an important task. A polygon can be regular (all sides equal) or irregular (different side lengths). The Area of a Polygon Calculator simplifies this task by taking the required inputs and returning accurate area results instantly.

This guide explains how the calculator works, the formulas used, and gives a step-by-step example.

Formula for Area of a Regular Polygon

A regular polygon has:

All sides equal
All angles equal
A known apothem (distance from the center to a side)

Formula

$\text{Area} = \frac{1}{2} \times \text{Perimeter} \times \text{Apothem}$

Alternate Formula for Regular Polygon (Using Side Length)

If you know the number of sides (n) and side length (s), the formula is:

Formula

$\text{Area} = \frac{n \times s^2}{4 \times \tan\left(\frac{\pi}{n}\right)}$

Formula for Area of an Irregular Polygon Using Coordinates

If the polygon is irregular, and all vertex coordinates are known, use the Shoelace Formula:

Formula

$\text{Area} = \frac{1}{2} \left| \sum_{i=1}^{n-1}(x_i y_{i+1}) + x_n y_1 - \sum_{i=1}^{n-1}(y_i x_{i+1}) - y_n x_1 \right|$

Example Calculation (Regular Polygon)

Example: Find the area of a regular hexagon (6 sides) where each side is 10 cm

Step 1: Identify values

n=6n = 6
n=6
s=10s = 10
s=10 cm

Step 2: Use the formula

$\text{Area} = \frac{n \times s^2}{4 \times \tan\left(\frac{\pi}{n}\right)}$

Step 3: Substitute values

$\text{Area} = \frac{6 \times 10^2}{4 \times \tan\left(\frac{\pi}{6}\right)}$

$\text{Area} = \frac{600}{4 \times 0.57735}$

$\text{Area} = \frac{600}{2.3094}$

$\text{Area} \approx 259.81\ \text{cm}^2$

FAQs

1. What is a polygon?

A polygon is a closed 2-dimensional shape made up of straight line segments. Examples include triangles, quadrilaterals, pentagons, hexagons, etc.

2. What is a regular polygon?

A regular polygon has all sides equal and all interior angles equal—like a square, equilateral triangle, or hexagon.

3. What is an irregular polygon?

An irregular polygon has unequal sides and unequal angles. Examples include random land boundaries or uneven geometric shapes.

4. What inputs do I need for an Area of a Polygon Calculator?

Depending on the polygon type, you need:

Number of sides
Length of each side
Apothem (for regular polygon)
Vertex coordinates (for irregular polygon)

5. Can I calculate area if the polygon is not regular?

Yes. Use the Shoelace Formula if you have coordinates of all vertices. The calculator can compute this automatically.

6. What is apothem?

The apothem is the perpendicular distance from the center of a regular polygon to any of its sides. It is required for perimeter × apothem formula.

7. Why do regular polygons use the tangent formula?

Regular polygons have symmetrical angles, so using trigonometric functions like tan(π/n) helps calculate the area using just the side length.

8. How do I find the area of a triangle using this calculator?

A triangle is a 3-sided polygon. If it is regular (equilateral), use the regular polygon formula. If irregular, input the coordinates or use standard triangle formula:

$\text{Area} = \frac{1}{2} \times \text{Base} \times \text{Height}$

9. Can this calculator be used for land measurement?

Yes. If you know the boundary coordinates of a land plot, the calculator can compute area using the coordinate-based method.

10. Can I calculate area using only side lengths?

Only for regular polygons. For irregular polygons, side lengths alone are not enough because angles vary.

11. Why is understanding polygon area important?

It is useful for construction planning, flooring, fencing, designing shapes, architecture, surveying, and land measurement.

12. Does the number of sides affect accuracy?

Yes. As the number of sides increases, calculating area manually becomes complex. A calculator method is far more accurate.

13. Can polygons have curved sides?

No. A polygon by definition always has straight line segments. Shapes with curves are not polygons.

Check out 2 Similar Calculators:

Perimeter Of Polygon Calculator

Area of a Polygon Calculator

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