Regular Polygon Area Calculator

About Regular Polygon Area Calculator

Regular polygon: all sides and angles equal. Interior angle = (n-2)×180/n. Area = ½ × perimeter × apothem.

How to use this calculator

1. Enter the number of sides of the regular polygon.
2. Enter the side length using the same unit for every side.
3. Click calculate to get the area.
4. Check the displayed formula and example to understand the result.

The formula explained

• \(\text{Area}\) = the area of the regular polygon
• \(n\) = the number of sides
• \(s\) = the length of one side
• \(\tan\) = the tangent function
• \(\pi\) = the constant pi

Step by step method

1. Count the sides to confirm the polygon is regular and has all sides equal.
2. Use the side length and the number of sides in the area formula.
3. Evaluate the tangent term for the given number of sides.
4. Multiply and divide to get the area in square units.

Worked example

Suppose you want the area of a regular hexagon with side length 6 cm.

1. For a hexagon, \(n = 6\) and \(s = 6\).
2. Substitute into the formula: \(\text{Area} = \frac{6 \cdot 6^2}{4 \tan(\pi/6)}\).
3. Since \(6^2 = 36\) and \(\tan(\pi/6) = \frac{1}{\sqrt{3}}\), the area is \(\frac{216}{4/\sqrt{3}} = 54\sqrt{3}\).
4. That is about 93.53 square cm.

Tips and common mistakes

• Make sure the polygon is regular, meaning all sides and angles are equal.
• Use one consistent unit for the side length, since the answer will be in square units.
• Double check the number of sides, because the formula changes with n.
• If you already know the perimeter or apothem, this tool is still useful when you have the side length.

Frequently asked questions