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 and the side length :
However, given other parameters, you can also find out the area:
- , having - incircle radius (it's also an apothem - a line segment from the center to the midpoint of one of its sides)
- , given and polygon perimeter
- , given
- , having - 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:
with and
-
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).
-
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.
FAQ
How do I calculate the area of a regular polygon given the radius?
To calculate the area of a regular polygon given the radius apply the formula:
area = n * a² * cot(π/n) / 4
Where:
n
is the number of sides of the polygon;a
is the length of the side; andcot
is the cotangent function (cot(x) = 1/tan(x)
).
What is the area of a pentagon with side 3?
15.484
. To compute the area of a pentagon with side 3, you can directly apply the formula:
area = n × a² × cot(π/n) / 4
,
substituting:
n = 5
; anda = 3
.
What is the formula for the area of a polygon given the apotheme?
If you know the apothem of a regular polygon you can compute the area with the formula:
area = ap² × n × tan(π/n)
Where:
ap
is the apothem (the segment connecting the side midpoint to the center); andn
is the number of sides of the regular polygon.
What is the area of a hexagon with side 0.7621 m
?
1.509 m²
. To calculate the area, use the formula for the area of a regular hexagon:
area = 6 × a² × cot(π/6) / 4
Where a
is the side length.
This particular hexagon is equal in size to any one of the 18 elements in the primary mirror of the James Webb Space Telescope.