Heptagon Area Calculator

Calculate the area of a regular heptagon with seven sides of equal length. Includes the formula, a worked example, and rare but useful applications.

Calculate area of heptagon

Regular heptagon:

\\text{area} = \\\\frac{7}{4} \\\\times s^2 \\\\times \\\\cot\left(\\\\frac{180°}{7}\right)

Approximation:

\\text{area} \\\\approx 3.6339 \\\\times s^2

Where s is the side length.

Calculate the area of a regular heptagon with side length 5 cm:

\\text{area} \\\\approx 3.6339 \\\\times 5^2 = 3.6339 \\\\times 25 = 90.85 \\\\text{ cm}^2

Result: 90.85 cm²

Perimeter: $7 \\\\times \\\\text{side}$
Apothem: $a = \\\\frac{s}{2 \\\\tan(25.71°)}$
Area with apothem: $\\\\frac{1}{2} \\\\times \\\\text{perimeter} \\\\times \\\\text{apothem}$

What if the heptagon is irregular? Divide it into triangles or use coordinate geometry.

What is the sum of interior angles? 900° for any heptagon.

Can I calculate from the radius? Yes, use $s = 2R \\\\sin(25.71°)$ to find the side first.

How many diagonals does a heptagon have? 14 diagonals.