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Area of Regular Polygon given Perimeter and Inradius Calculator

Formula

The formula to calculate the Area of Regular Polygon (A) is:

$A = \frac{P \cdot ri}{2}$

Where:

$A$ is the Area of Regular Polygon (measured in Square Meters).
$P$ is the Perimeter of Regular Polygon (measured in Meters).
$ri$ is the Inradius of Regular Polygon (measured in Meters).

Definition

The Area of Regular Polygon is the total region or space enclosed inside the polygon.

The Perimeter of Regular Polygon is the total distance around the edge of the Regular Polygon.

The Inradius of Regular Polygon is the line connecting the center of the polygon to the midpoint of one of the Regular Polygon's sides. The inradius is also the radius of the incircle.

How to calculate Area of Regular Polygon

Let's assume the following values:

Perimeter of Regular Polygon (P) = 80 Meters
Inradius of Regular Polygon (ri) = 12 Meters

Using the formula:

$A = \frac{80 \cdot 12}{2}$

Evaluating:

$A \approx 480$

The Area of Regular Polygon is approximately 480 Square Meters.

Conversion Chart

Perimeter (P) (Meters)	Inradius (ri) (Meters)	Area (A) (Square Meters)
60	10	300.000000000000
60	12	360.000000000000
60	14	420.000000000000
80	10	400.000000000000
80	12	480.000000000000
80	14	560.000000000000
100	10	500.000000000000
100	12	600.000000000000
100	14	700.000000000000