Regular Polygon Area Calculator

How to use the regular polygon area calculator

The regular polygon area calculator is an essential tool for students, teachers, architects, and engineers who need to calculate the area of regular polygonal surfaces. This calculator uses an advanced geometry formula to calculate the area based on the number of sides and side length.

1. Determine the number of sides of the regular polygon
2. Accurately measure the length of one of the polygon's sides
3. Enter the obtained values in the corresponding fields, using meters as the unit of measurement
4. Click the 'Calculate' button to get the result in square meters
5. Use the share or print buttons to save or send the result

Regular polygon area calculation formula

The calculation of a regular polygon's area is performed using a formula that relates the number of sides and the side length. This formula is derived from decomposing the polygon into triangles.

This formula considers that:

• n is the number of sides of the polygon
• s is the length of each side
• π (pi) is the mathematical constant approximately equal to 3.14159

Practical calculation examples

For better understanding, let's analyze some practical examples of area calculation:

• Regular pentagon (5 sides) with side of 4m. Area = (5 × 4²) / (4 × tan(π/5)) = 27.53m²
• Regular hexagon (6 sides) with side of 5m. Area = (6 × 5²) / (4 × tan(π/6)) = 64.95m²
• Regular octagon (8 sides) with side of 3m. Area = (8 × 3²) / (4 × tan(π/8)) = 43.46m²

Frequently Asked Questions (FAQ)