Calculadora de Área do Pentágono
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
A = (l²·√(25 + 10·√5)) / 4
About this calculator
The Pentagon Area Calculator computes the area of a regular pentagon using the side length. The formula is A = (l² * √(25 + 10√5)) / 4, where l is the side. This expression comes from decomposing the pentagon into isosceles triangles, combining geometry and trigonometry. The result is in square units, such as cm² or m², based on the side unit.
Use this calculator whenever you need the area of a regular pentagon, for example in architectural projects, design of pentagonal objects, or geometry problems. For instance, to calculate the amount of paint for a pentagonal tabletop, or to size a garden bed shaped like a pentagon. The tool is useful for students, engineers, and professionals working with geometric shapes.
Caution: the calculator works only for regular pentagons, i.e., with equal sides and internal angles of 108°. If the pentagon is irregular, the formula does not apply. Ensure you measure the side accurately and use the same unit for input. Also, the calculation involves the square root of an irrational number, so the result may be approximate.
Frequently asked questions
What is a regular pentagon?
It is a five-sided polygon with all sides equal and all internal angles measuring 108°.
Can I use this calculator for irregular pentagons?
No, the formula only applies to regular pentagons. For irregular ones, you need to divide the shape into triangles and calculate separately.
What unit should I use for the side?
Use any length unit (cm, m, inches, etc.). The area will be in the corresponding square unit.
Why does the formula have a square root of 5?
The square root of 5 appears due to the geometric properties of the pentagon, especially the golden ratio involved in its diagonals.
How can I check if my pentagon is regular?
Measure all sides: they must be equal. The internal angles, if measured, should be 108°.