The Area of Regular Polygon Calculator is a specialized tool designed to compute the area of a polygon with equal-length sides and equal angles between those sides. By inputting the number of sides (n) and the apothem (a) — the distance from the center to the midpoint of a side — the calculator quickly determines the area. This tool is invaluable for anyone needing to solve geometry problems efficiently and accurately, removing the complexity of manual calculations.
Formula of Area of Regular Polygon Calculator
To calculate the area of a regular polygon, use the following formula:
Area = (n * a^2) / (4 * tan(π / n))
- n is the number of sides of the regular polygon.
- a is the apothem of the polygon.
Steps:
- Gather information:
- Determine the number of sides (n) of the regular polygon.
- Measure the apothem (a) of the polygon.
- Calculate the area:
- Substitute the values of n and a into the formula and simplify.
- Alternative method:
- Use a calculator with tan function capability.
- Follow the sequence: Enter n, square it, multiply by a squared, divide by 4, and finally divide by tan(π / n).
- Interpret the result:
- The area result will be in the same units squared as the apothem (a).
General Reference Table for Regular Polygon Areas
| Number of Sides (n) | Polygon Name | Area (square units) |
|---|---|---|
| 3 | Equilateral Triangle | Approx. 259.81 |
| 4 | Square | 400 |
| 5 | Pentagon | Approx. 688.19 |
| 6 | Hexagon | Approx. 1039.23 |
| 7 | Heptagon | Approx. 1428.86 |
| 8 | Octagon | Approx. 1853.85 |
| 9 | Nonagon | Approx. 2313.06 |
| 10 | Decagon | Approx. 2805.40 |
Note: The areas listed are calculated using the formula Area = (n * a^2) / (4 * tan(π / n)) with a = 10 units. The results are rounded to two decimal places for clarity. These values provide a quick way to understand how the area increases with the number of sides for a given apothem length.
Example of Area of Regular Polygon Calculator
To illustrate, consider a regular hexagon (n = 6) with an apothem of 10 units. Using the formula:
Area = (6 * 10^2) / (4 * tan(π / 6))
The calculated area provides a precise measurement in square units, facilitating accurate planning and design in practical applications.
Most Common FAQs
The apothem is crucial as it represents the radius of an inscribed circle within the polygon, directly influencing the area calculation.
No, this formula is specifically design for regular polygons where all sides and angles are equal. Irregular polygons require different methods for area calculation.
Increasing the number of sides while keeping the apothem constant will increase the area, showing how polygons approximate a circle more closely as the side count grows.