A Regular Polygon is a shape where all sides are the same length and all interior angles are equal. From the three-sided Equilateral Triangle to the millions-sided "Megagon", these shapes are the building blocks of geometry. The Regular Polygon Area Calculator allows you to solve for the area of *any* -sided regular shape instantly, without needing complex trigonometry.
Formulas for N-Sided Shapes
There are three main ways to calculate the area () of a regular polygon with sides.
1. Using Side Length (s)
This is the most common method. If you measure the flat edge:
2. Using Apothem (a)
The Apothem is the distance from the center of the polygon to the midpoint of a side (at 90 degrees).
3. Using Radius (R)
The Circumradius is the distance from the center to a vertex (corner).
Real World Applications
Architecture & Tiling
Hexagons () and Octagons () are famous for their ability to tile floors (tessellation). Architects use these area calculations to estimate the square footage of gazebos, courtyards, and towers.
Manufacturing & Engineering
Bolts, nuts, and wrench sockets are standard regular polygons (usually Hexagons). Calculating the cross-sectional area is vital for determining the shear strength of the fastener.
Game Design
In video game rendering, approximate circles are often drawn as regular polygons with many sides (e.g., or ). Calculating the area of these "low-poly" circles helps in physics collision detection.
Frequently Asked Questions (FAQ)
1. What if my sides are not equal?
Then it is an Irregular Polygon. You cannot use the formulas above. You must use the "Polygon Coordinates Calculator" or split the shape into triangles.
2. What is the angle of a regular polygon?
The internal angle of any regular polygon is calculated as: . For a Hexagon (), it is .
3. Can I calculate a Dodecagon?
Yes! Simply set the "Number of Sides" to 12. You can calculate finding the area of a 100-sided Hectogon if you like!
Final Words
Nature loves efficiency, and regular polygons are the most efficient shapes in existence. Use the Regular Polygon Area Calculator to decode the math of the honeycomb and the star.
