The area of a regular pentagon is the space enclosed inside its five equal sides. Pentagons appear in industrial design, architecture, and math — and they are closely linked to the golden ratio and the five-pointed star.

The Formula

A = (5 × t²) / (4 × tan(π/5))

• A — area of the pentagon (cm², m², etc.)
• 5 — number of sides
• t — side length
• tan(π/5) — tangent of 36°, approximately 0.72654

The formula comes from splitting the pentagon into five equal isosceles triangles from the center and adding up all their individual areas.

Step-by-Step Example