Regular Polygon Area Calculator: Find the Area of Any Regular Polygon
ByMuhammad Ali•Founder of KruskalCode
17:26
6 min read
Understanding how to calculate the area of a regular polygon is a fundamental skill in geometry. Whether you're dealing with a simple square, a hexagon, or a polygon with many sides, the principle remains the same. This guide will walk you through the formula, provide examples, and show you how our Regular Polygon Area Calculator makes the process straightforward.
Explanation
A regular polygon is a two-dimensional shape where all its sides are of equal length, and all its interior angles are equal. Common examples include equilateral triangles (3 sides), squares (4 sides), regular pentagons (5 sides), and regular hexagons (6 sides). The area of such a polygon can be found using a specific formula that incorporates the number of sides and the length of one side. This formula is derived from dividing the polygon into congruent isosceles triangles, with their vertices meeting at the polygon's center.
Formula
The formula to calculate the area of a regular polygon when you know the number of sides (n) and the length of one side (s) is: Area = (n × s²) / (4 × tan(π/n)) Where: - n represents the number of sides of the polygon. - s represents the length of one side of the polygon. - π (Pi) is a mathematical constant, approximately 3.14159. - tan is the tangent function, and π/n is an angle in radians.
Example
Let's calculate the area of a regular pentagon with a side length of 7 cm. A pentagon has 5 sides, so n = 5. The side length s = 7 cm. Using the formula: Area = (5 × 7²) / (4 × tan(π/5)) Area = (5 × 49) / (4 × tan(0.6283 radians)) Area = 245 / (4 × 0.7265) Area = 245 / 2.906 Area ≈ 84.37 square cm. This means a regular pentagon with 7 cm sides covers an area of approximately 84.37 square centimeters.
How to use the related calculator
Using the ProMathTools Regular Polygon Area Calculator is simple. First, locate the 'Number of Sides (n)' input field and type in the total number of sides your polygon has (e.g., '5' for a pentagon). Next, find the 'Side Length (s)' field and enter the length of one of its sides (e.g., '7'). Once both values are entered, the calculator will instantly display the calculated area in square units, helping you verify your homework or solve real-world geometry problems.
Try the related calculator
Open toolFAQ
Why does the formula use tangent?
The tangent function is used because the formula effectively breaks the regular polygon into 'n' identical isosceles triangles. The tangent helps relate the side length to the apothem (the distance from the center to the midpoint of a side), which is crucial for calculating the area of these triangles and, by extension, the entire polygon.
Can I use this for shapes like circles or ellipses?
No, this calculator is specifically for regular polygons. Circles and ellipses are not polygons; they have curved boundaries and require different formulas for calculating their area. For circles, you would use Area = πr².
What are the units for the area?
The units for the area will be the square of whatever unit you use for the side length. For example, if your side length is in meters, the area will be in square meters (m²). If your side length is in inches, the area will be in square inches (in²).
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About the author
Muhammad Ali. Muhammad Ali is a full-stack developer and founder of KruskalCode. He builds SaaS platforms and automation systems with React and Laravel, and helps teams ship fast, scalable tools.
Need a custom calculator, dashboard, or automation workflow? Reach out to KruskalCode.
