Area of a Regular Polygon Calculator
This area of a regular polygon calculator can help - as you can guess - in determining the area of a regular polygon. Type the number of sides and the polygon area appears in no time. If you're wondering how to find the area of a polygon formula, keep reading and you'll find the answer! If you want to calculate the area of any 3-sided or 4-sided polygon, check out this triangle area and quadrilateral area calculator.
Area of a regular polygon formulas
The most popular, and usually the most useful formula is the one that uses the number of sides n and the side length a:
area = n * a² * cot(π/n) / 4
However, given other parameters, you can also find out the area:
area = n * a * ri / 2, havingri- incircle radius (it's also an apothem - a line segment from the center to the midpoint of one of its sides)area = perimeter * ri / 2, givenriand polygon perimeterarea = n * (ri)² * tan(π/n), givenriarea = n * (rc)² * sin(2π/n) / 2, havingrc- circumcircle radius
How to find the area of a polygon?
If you want to find the area of a regular polygon, simply use the formulas described above. However, if the polygon is not regular (what means it isn't equiangular and equilateral), you can:
- Find the area using vertices coordinates:
area = |Σ(xᵢ * yᵢ₊₁) - (yᵢ * xᵢ₊₁)| / 2
with x(n+1) → x(1) and y(n+1) → y(1)
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Determine the polygon area given side lengths and some diagonals, by splitting the polygon into triangles. Then find the area with given three sides (SSS) equation (it's called Heron's formula).
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Calculate the area of polygons using other formulas - e.g. for a scalene triangle or a quadrilateral.
Using the area of regular polygon calculator: an example
Let's assume that you want to calculate the area of a specific regular polygon, e.g. 12-sided polygon, dodecagon with 5-inch sides.
- Enter the number of sides of chosen polygon. Put 12 into the number of sides box.
- Type in the polygon side length. In our example, it's equal to 5 in.
- Our area of polygon calculator displays the area. It's 279.9 in².
If you want to calculate the area of a regular polygon using other parameters than the side length, check out this general regular polygon calculator.