n$. What is the easiest formula for the area of a regular N-gon? The easiest conceptual formula is $\\text{Area} = \frac{1}{2} a P$, where $a$ is the apothem and $P$ is the perimeter ($P = n \cdot s$). The most direct formula using only the side length $s$ and number of sides $n$ is: $\\text{Area} = \frac{1}{4} n s^2 \cot(\\frac{180^\circ}{n})$. Key Polygon Formulas Area $$A = \frac{1}{2} a P$$ Internal Angle $$\theta_i = \frac{(n-2)180^\circ}{n}$$ Apothem (from Side $s$) $$a = \frac{s}{2 \tan\left(\frac{180^\circ}{n}\right)}$$ Related Geometry Tools Regular Polygon Calculator (General) Pentagon Calculator Hexagon Calculator Octagon Calculator Area Calculator (General)

Calculators in n$. What is the easiest formula for the area of a regular N-gon? The easiest conceptual formula is $\\text{Area} = \frac{1}{2} a P$, where $a$ is the apothem and $P$ is the perimeter ($P = n \cdot s$). The most direct formula using only the side length $s$ and number of sides $n$ is: $\\text{Area} = \frac{1}{4} n s^2 \cot(\\frac{180^\circ}{n})$. Key Polygon Formulas Area $$A = \frac{1}{2} a P$$ Internal Angle $$\theta_i = \frac{(n-2)180^\circ}{n}$$ Apothem (from Side $s$) $$a = \frac{s}{2 \tan\left(\frac{180^\circ}{n}\right)}$$ Related Geometry Tools Regular Polygon Calculator (General) Pentagon Calculator Hexagon Calculator Octagon Calculator Area Calculator (General).