Area of Regular Polygon Calculator [ Find Regular Polygon Area ]
To calculate the area of a regular polygon, square the side length (s²) and multiply by the number of sides (n). Divide this product by 4 times the tangent of π/n. This will give you the area of the polygon.
Area of Regular Polygon Calculator
The Area of Regular Polygon Calculator is designed to help you quickly find the area of any regular polygon by inputting the number of sides and the length of each side. Whether you’re calculating the area of a 5-sided polygon or a polygon with 16 sides, this tool uses the standard formulas to provide accurate results.
You can also calculate the area using an apothem or radius if given. The calculator is ideal for students, architects, and anyone working with polygons in geometry. It simplifies the process, giving step-by-step results for calculating the area of both regular and irregular polygons.
Formula:
| Variable | Meaning |
|---|---|
| A | Area of the regular polygon |
| n | Number of sides of the polygon |
| s | Length of each side |
| π | Pi (approximately 3.14159) |
Solved Calculations:
Example 1:
Given Values:
- n = 6 sides (hexagon)
- s = 5 meters
| Calculation | Instructions |
|---|---|
| A = (6 × 5²) / (4 × tan(π / 6)) | Square the side length and multiply by the number of sides. Divide by 4 times the tangent of π/n. |
| A = (6 × 25) / (4 × tan(π / 6)) | Calculate the side length squared. |
| A = 150 / (4 × tan(0.5236)) | Calculate π/6 and then find the tangent. |
| A = 150 / (4 × 0.5774) | Multiply by the number of sides. |
| A = 150 / 2.3096 | Perform the final division. |
| A ≈ 64.95 square meters | The result gives the area of the hexagon. |
Answer: A ≈ 64.95 square meters
Example 2:
Given Values:
- n = 8 sides (octagon)
- s = 3 meters
| Calculation | Instructions |
|---|---|
| A = (8 × 3²) / (4 × tan(π / 8)) | Square the side length and multiply by the number of sides. Divide by 4 times the tangent of π/n. |
| A = (8 × 9) / (4 × tan(π / 8)) | Calculate the side length squared. |
| A = 72 / (4 × tan(0.3927)) | Calculate π/8 and then find the tangent. |
| A = 72 / (4 × 0.4142) | Perform the multiplication. |
| A = 72 / 1.6568 | Perform the final division. |
| A ≈ 43.45 square meters | The result gives the area of the octagon. |
Answer: A ≈ 43.45 square meters
What is Area of Regular Polygon Calculator | Easily Estimate Regular Polygon Area With This Calculator 2025
Finding the area of a regular polygon involves knowing the number of sides and the length of each side. This calculator uses an accurate formula to give you correct results for any polygon shape, whether you’re working with a 4-sided or 8-sided polygon.
This calculator can also be used with additional inputs, like the apothem, to provide an alternative method of calculating area.
For more complex shapes, like irregular polygons, tools like the Area of Irregular Polygon Calculator provide similar results by breaking down the polygon into triangles and calculating each area separately.
This calculator explains with Steps so that you easily understand the calculations behind the results.
Whether you’re dealing with an n-sided polygon or a polygon with given angles, this tool is flexible enough to handle various input formats.
From geometry homework to real-world applications, it is a must-have for accurate and efficient calculations.
