Area formulas of regular polygons

The s is the length of side in all polygons.

Equilateral triangle area

Number of sides = 3

\[ A = \frac{ \sqrt{3} }{4} s^2 \]

Square area

Number of sides = 4

\[ A = s^2 \]

Regular pentagon area

Number of sides = 5

\[ A = \frac{ \sqrt{ 25 + 10 \sqrt{5} } }{4} s^2 \]

Regular hexagon area

Number of sides = 6

\[ A = \frac{ 3 \sqrt{ 3 } }{ 2 } s^2 \]

Regular octagon area

Number of sides = 8

\[ A = ( 2 + 2 \sqrt{ 2 } ) s^2 \]

Regular decagon area

Number of sides = 10

\[ A = \frac{ 5 \sqrt{ 5 + 2 \sqrt{ 5 } } }{ 2 } s^2 \]

Regular dodecagon area

Number of sides = 12

\[ A = ( 6 + 3 \sqrt{ 3 } ) s^2 \]