Área Eneágono Regular
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
(9/4)·l²·cot(π/9)
About this calculator
The regular nonagon area calculator determines the area of a nine-sided polygon with equal sides. The calculation uses the formula (9/4)·l²·cot(π/9), where l is the side length. The cotangent of π/9 is a constant, approximately 2.7475. Simply input the side length and the area is computed instantly.
This tool is useful for geometry students, engineers, and architects who need to compute areas of regular polygonal shapes. For instance, when designing decorative pieces, floors, or structures with a nonagonal shape, the area is essential for estimating materials such as paint, ceramic tiles, or metal.
Important precautions: the formula applies only to regular nonagons (equal sides and angles). Ensure the polygon is truly regular. Also, the side length unit must be consistent (meters, centimeters, etc.) to obtain the area in the corresponding square unit. Small typing errors in the side length can cause large differences in the result.
For irregular nonagons, this calculator does not apply. In that case, you need to decompose the figure into triangles or use other methods. The calculator is an educational and practical tool, but always verify the problem context.
Frequently asked questions
What is a regular nonagon?
It is a nine-sided polygon with all sides and interior angles equal. Each interior angle measures 140°.
How to use the calculator if the side is in centimeters?
Simply enter the value in centimeters. The area will be displayed in square centimeters.
Does the formula work for irregular nonagons?
No, the formula is specific to regular nonagons. For irregular ones, another method is needed.
What is the value of cot(π/9)?
Approximately 2.747477419. The calculator uses this value internally.
Can I use this calculator for a 9-sided polygon with different side lengths?
No, the calculator requires equal sides. For different sides, the area must be calculated by decomposition.