Find regular pentagon area, perimeter, and apothem
Result
Pentagon Area
Step-by-Step Derivation
Pentagon Area Formula
A = 1/4 √(5(5 + 2√5))s²
A regular pentagon has five equal sides and five equal angles. Because the shape is regular, one side length determines the area, perimeter, and apothem.
⚠This calculator is for regular pentagons only. Side length must be positive.
How Pentagon Area Works
A regular pentagon can be split into five congruent isosceles triangles from the center. Combining those triangle areas gives the side-length formula.
Regular Shape
All sides and angles are equal.
Side Length
One side controls the full size.
Perimeter
Perimeter equals 5s.
Apothem
Center-to-side distance helps verify area.
💡 Example: For s=6, area is about 61.937, perimeter is 30, and apothem is 4.129.
Applications of Pentagon Area
ArchitectureBadge DesignTilingGeometry Homework
Frequently Asked Questions
What is a pentagon area calculator?▼
It calculates the area of a regular pentagon from its side length.
What is the regular pentagon area formula?▼
A common formula is A = 1/4√(5(5+2√5))s².
How do I use this calculator?▼
Enter the side length and click Calculate to get area, perimeter, and apothem.
Does this work for irregular pentagons?▼
No. This calculator assumes all five sides and angles are equal.
Where is pentagon area used?▼
It is used in geometry, architecture, tiling, icons, badges, and design layouts.
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