Regular Polygon Side Length from Area

Enter the number of sides and the area of a regular polygon to get the side length, perimeter, inradius, and circumradius.

Input

Enter the number of sides and the area of a regular polygon to find the side length. The perimeter, inradius, and circumradius are also shown.

Number of sides n

Area S

Side length a

6.204032

Perimeter

37.224194

Inradius r

5.37285

Circumradius R

6.204032

The length unit corresponds to the square root of the area unit. For example, if the area is in square centimeters, lengths are in centimeters.

The area of a regular n-gon is S equals n times a squared divided by 4 tan(pi/n). Solving for the side a gives a equals the square root of 4S tan(pi/n) over n.
The perimeter is n times a, the inradius (apothem) is r equals a divided by 2 tan(pi/n), and the circumradius is R equals a divided by 2 sin(pi/n).
The number of sides n must be an integer of 3 or more, and the area S must be positive.
The length unit corresponds to the square root of the area unit you enter.

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