Perimeter of Regular Polygon given Number of Sides and Inradius Calculator

✖The Number of Sides of Regular Polygon denotes the total number of sides of the Polygon. The number of sides is used to classify the types of polygons.ⓘ Number of Sides of Regular Polygon [N_S]			+10% -10%
✖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.ⓘ Inradius of Regular Polygon [r_i]			+10% -10%

✖The Perimeter of Regular Polygon is the total distance around the edge of the Regular Polygon.ⓘ Perimeter of Regular Polygon given Number of Sides and Inradius [P]

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Perimeter of Regular Polygon given Number of Sides and Inradius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Perimeter of Regular Polygon = 2*Number of Sides of Regular Polygon*Inradius of Regular Polygon*tan(pi/Number of Sides of Regular Polygon)
P = 2*N_S*r_i*tan(pi/N_S)
This formula uses 1 Constants, 1 Functions, 3 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

tan - The tangent of an angle is a trigonometric ratio of the length of the side opposite an angle to the length of the side adjacent to an angle in a right triangle., tan(Angle)

Variables Used

Perimeter of Regular Polygon - (Measured in Meter) - The Perimeter of Regular Polygon is the total distance around the edge of the Regular Polygon.
Number of Sides of Regular Polygon - The Number of Sides of Regular Polygon denotes the total number of sides of the Polygon. The number of sides is used to classify the types of polygons.
Inradius of Regular Polygon - (Measured in Meter) - 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.

STEP 1: Convert Input(s) to Base Unit

Number of Sides of Regular Polygon: 8 --> No Conversion Required
Inradius of Regular Polygon: 12 Meter --> 12 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

P = 2*N_S*r_i*tan(pi/N_S) --> 2*8*12*tan(pi/8)

Evaluating ... ...

P = 79.5290039756343

STEP 3: Convert Result to Output's Unit

79.5290039756343 Meter --> No Conversion Required

FINAL ANSWER

79.5290039756343 ≈ 79.529 Meter <-- Perimeter of Regular Polygon

(Calculation completed in 00.004 seconds)

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< Perimeter of Regular Polygon Calculators

Perimeter of Regular Polygon given Number of Sides and Circumradius

LaTeX Go Perimeter of Regular Polygon = 2*Circumradius of Regular Polygon*Number of Sides of Regular Polygon*sin(pi/Number of Sides of Regular Polygon)

Perimeter of Regular Polygon given Number of Sides and Inradius

LaTeX Go Perimeter of Regular Polygon = 2*Number of Sides of Regular Polygon*Inradius of Regular Polygon*tan(pi/Number of Sides of Regular Polygon)

Perimeter of Regular Polygon given Circumradius and Area

LaTeX Go Perimeter of Regular Polygon = (2*Area of Regular Polygon)/sqrt(Circumradius of Regular Polygon^2-Edge Length of Regular Polygon^2/4)

Perimeter of Regular Polygon

LaTeX Go Perimeter of Regular Polygon = Number of Sides of Regular Polygon*Edge Length of Regular Polygon

Perimeter of Regular Polygon given Number of Sides and Inradius Formula

LaTeX Go

Perimeter of Regular Polygon = 2*Number of Sides of Regular Polygon*Inradius of Regular Polygon*tan(pi/Number of Sides of Regular Polygon)
P = 2*N_S*r_i*tan(pi/N_S)

What is Regular polygon?

A Regular Polygon has sides of equal length and equal angles between each side. A regular n-sided polygon has rotational symmetry of order n and it is also known as a cyclic polygon. All the vertices of a regular polygon lie on the circumscribed circle.

How to Calculate Perimeter of Regular Polygon given Number of Sides and Inradius?

Perimeter of Regular Polygon given Number of Sides and Inradius calculator uses Perimeter of Regular Polygon = 2*Number of Sides of Regular Polygon*Inradius of Regular Polygon*tan(pi/Number of Sides of Regular Polygon) to calculate the Perimeter of Regular Polygon, The Perimeter of Regular Polygon given Number of Sides and Inradius formula can be defined as the total distance around the edge of the Regular Polygon, calculated using its inradius and number of sides. Perimeter of Regular Polygon is denoted by P symbol.

How to calculate Perimeter of Regular Polygon given Number of Sides and Inradius using this online calculator? To use this online calculator for Perimeter of Regular Polygon given Number of Sides and Inradius, enter Number of Sides of Regular Polygon (N_S) & Inradius of Regular Polygon (r_i) and hit the calculate button. Here is how the Perimeter of Regular Polygon given Number of Sides and Inradius calculation can be explained with given input values -> 79.529 = 2*8*12*tan(pi/8).

FAQ

What is Perimeter of Regular Polygon given Number of Sides and Inradius?

The Perimeter of Regular Polygon given Number of Sides and Inradius formula can be defined as the total distance around the edge of the Regular Polygon, calculated using its inradius and number of sides and is represented as P = 2*N_S*r_i*tan(pi/N_S) or Perimeter of Regular Polygon = 2*Number of Sides of Regular Polygon*Inradius of Regular Polygon*tan(pi/Number of Sides of Regular Polygon). The Number of Sides of Regular Polygon denotes the total number of sides of the Polygon. The number of sides is used to classify the types of polygons & 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 Perimeter of Regular Polygon given Number of Sides and Inradius?

The Perimeter of Regular Polygon given Number of Sides and Inradius formula can be defined as the total distance around the edge of the Regular Polygon, calculated using its inradius and number of sides is calculated using Perimeter of Regular Polygon = 2*Number of Sides of Regular Polygon*Inradius of Regular Polygon*tan(pi/Number of Sides of Regular Polygon). To calculate Perimeter of Regular Polygon given Number of Sides and Inradius, you need Number of Sides of Regular Polygon (N_S) & Inradius of Regular Polygon (r_i). With our tool, you need to enter the respective value for Number of Sides of Regular Polygon & Inradius of Regular Polygon and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Perimeter of Regular Polygon?

In this formula, Perimeter of Regular Polygon uses Number of Sides of Regular Polygon & Inradius of Regular Polygon. We can use 3 other way(s) to calculate the same, which is/are as follows -

Perimeter of Regular Polygon = Number of Sides of Regular Polygon*Edge Length of Regular Polygon
Perimeter of Regular Polygon = 2*Circumradius of Regular Polygon*Number of Sides of Regular Polygon*sin(pi/Number of Sides of Regular Polygon)
Perimeter of Regular Polygon = (2*Area of Regular Polygon)/sqrt(Circumradius of Regular Polygon^2-Edge Length of Regular Polygon^2/4)

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