Regular Polygon Area and Perimeter
Regular Polygon Area and Perimeter
\[\begin{aligned}
A &= \frac{P*a}{2} \\
P &= n*s
\end{aligned}\]
Variables
A = area
P = perimeter
n = number of sides
s = side length
a = apothem
r = circumradius
Description
What is this formula?
This set of formulas calculates the area and perimeter of a regular polygon using its side length, number of sides, and apothem.
When to use it
Use these formulas in geometry, engineering, architecture, and design whenever working with polygons that have equal sides and equal angles.
Example
For a regular hexagon with 6 sides of 4 m and apothem 3.46 m:
Perimeter:
P = 6*4 = 24 m
Area:
A = (24*3.46)/2 = 41.52 m²
Applications
- Architectural floor plans
- Mechanical and industrial design
- Geometric analysis
- CAD and technical drawing
- Tiling and decorative patterns
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