Polygon Side Length from Area

s = \sqrt{\frac{(4 \cdot tan (\frac{π}{n})) \cdot A}{n}}

$s = sqrt(((4* tan(pi/ "n" ))* "A" )/ "n" )$

(n) Number of Polygon Sides

$(n)"Number of Polygon Sides"$

(A) Area inside the polygon

$(A)"Area inside the polygon"$

The Math / Science

A regular n-sided polygon is a polygon with n equal length sides and is a polygon which has n equal angles at the n vertices of the polygon. This formula uses the polygon area equation:

$A = \frac{n \cdot s}{4 \cdot tan (\frac{π}{n})}$ $A = (n * s) / (4 * tan(pi/n))$ to solve for s. This is the length of a side corresponding with a polygon of n sides and an area of A. The circumference is simply stated as follows:

$Polygon Circumference = s \cdot n$ $"Polygon Circumference" = s * n$

Regular Polygon Information

A regular polygon is a geometric shape with three or more straight sides where every side is the same length and every angle between connecting sides are the same angle. Because of the symmetry of the regular polygon, all the vertices of the polygon can be constructed to touch a circle in which the regular polygon is inscribed and all the chords that are polygon sides will then obviously be of equal length . Likewise, because of the regular polygon's symmetry, a circle constructed to be inscribed in a regular polygon and touching the polygon will touch the regular polygon at the midpoint of the polygon side. As shown in the pictures, Figure 1 and Figure 2, lines from the regular polygon's vertices to the circle's center form n isosceles triangles of equal area.

The names of polygons vary based on the number of sides as follows:

triangle - 3 sides
square - 4 sides
pentagon - 5 sides
hexagon - 6 sides
heptagon - 7 sides
octagon - 8 sides
nonagon - 9 sides
decagon - 10 sides
hendecagon - 11 sides
dodecagon - 12 sides

Common Regular Polygon Functions

Polygon Area Calculators:

Polygon Side Calculators

Polygon Perimeter Calculators

Polygon Radius

Radius of Circle around a Polygon

3D Polygon Shapes

Polygon Ring Volume

Other Polygon Calculators

Interior Angle of a Regular Polygon based on the number of sides
Area of Circle - Circle approximates a polygon as the number of sides approaches infinity.
Area of Triangle - Three Sides
Area of a Square - Four Sides
Area of Pentagon - Five Sides
Area of Hexagon - Six Sides
Area of Heptagon - Seven Sides
Area of Octagon - Eight Sides
Area of Nonagon - Nine Sides
Area of Decagon - Ten Sides
Area of Hendecagon - Eleven Sides
Area of Dodecagon - Twelve Sides