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# Regular Polygons

## Areas of regular polygons - polygons with 3 to 12 sides.

### Perimeter of a Regular Polygon

P = n a                                 (1)

where

P = perimeter (m, ft ..)

n = number of sides

a = length of side (m, ft, ..)

### Area of a Regular Polygon

A = n a r / 2

= n r2 tan(Θ)

= n R2 sin(2 Θ) / 2                                (2)

Regular Polygons - Area vs. Number of Sides
PolygonNumber of Sides
- n -
Area
(m2, ft2 ..)
Triangle, equilateral 3 0.4330 a2
Square 4 1.0000 a2
Pentagon 5 1.7205 a2
Hexagon 6 2.5981 a2
Heptagon 7 3.6339 a2
Octagon 8 4.8284 a2
Nonagon 9 6.1818 a2
Decagon 10 7.6942 a2
Undecagon 11 9.3656 a2
Dodecagon 12 11.1961 a2

## Related Topics

• ### Mathematics

Mathematical rules and laws - numbers, areas, volumes, exponents, trigonometric functions and more.

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• ### Center of Gravity

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Calculate chord lengths when dividing the circumference of a circle into an equal number of segments.
• ### Hexagons and Squares - Diagonal Lengths

Distances between corners for hexagons and squares.
• ### Oblique Triangle

Calculate oblique triangles.
• ### Pythagorean Theorem

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• ### Right Angled Triangle

Right angled triangle equations.

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## Citation

• The Engineering ToolBox (2014). Regular Polygons. [online] Available at: https://www.engineeringtoolbox.com/regular-polygons-area-d_1872.html [Accessed Day Month Year].

Modify the access date according your visit.

6.3.17

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