Regular Polygon Area Calculator
Use this calculator to determine the area of any regular polygon. A regular polygon is a polygon that is equiangular (all angles are equal in measure) and equilateral (all sides have the same length).
Calculated Area:
Enter values and click 'Calculate Area'.
Understanding Regular Polygons and Their Area
A polygon is a closed two-dimensional shape made up of straight line segments. When all sides of a polygon are equal in length and all interior angles are equal in measure, it is called a regular polygon. Common examples include equilateral triangles, squares, regular pentagons, and hexagons.
Why Calculate Polygon Area?
Calculating the area of a regular polygon is essential in various fields:
- Architecture and Construction: For designing structures, calculating material needs for flooring, roofing, or wall sections that are polygonal.
- Engineering: In mechanical design, for components with polygonal cross-sections.
- Art and Design: For creating patterns, tessellations, or understanding spatial arrangements.
- Mathematics and Geometry: As a fundamental concept in geometry, used for solving more complex problems.
The Formula for Regular Polygon Area
The area of a regular polygon can be calculated using the number of sides and the length of one side. The formula is:
Area = (n * s²) / (4 * tan(π / n))
Where:
n= Number of sidess= Length of one sideπ(Pi) ≈ 3.14159tan= Tangent function
This formula is derived from dividing the regular polygon into 'n' congruent isosceles triangles, calculating the area of one such triangle, and multiplying by 'n'. The tangent function is used to find the apothem (the distance from the center to the midpoint of a side) of the polygon.
How to Use This Calculator
- Number of Sides: Enter the total number of sides your regular polygon has. This must be an integer of 3 or greater (e.g., 3 for a triangle, 4 for a square, 5 for a pentagon, 6 for a hexagon).
- Side Length: Input the length of one side of the polygon. Since it's a regular polygon, all sides are of equal length.
- Calculate: Click the "Calculate Area" button. The calculator will instantly display the area of your regular polygon in "square units".
Example Calculation
Let's calculate the area of a regular hexagon with a side length of 10 units:
- Number of Sides (n) = 6
- Side Length (s) = 10
Using the formula:
Area = (6 * 10²) / (4 * tan(π / 6))
Area = (6 * 100) / (4 * tan(0.5235987756 radians))
Area = 600 / (4 * 0.57735)
Area = 600 / 2.3094
Area ≈ 259.81 square units
This calculator simplifies this process, providing quick and accurate results for your regular polygon area calculations.