Edge Length of Regular Polygon given Inradius Calculator

✖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 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%

✖The Edge Length of Regular Polygon is the length of one of the sides of the Regular Polygon.ⓘ Edge Length of Regular Polygon given Inradius [l_e]

⎘ Copy

👎

Formula

✖

Edge Length of Regular Polygon given Inradius

Formula

`"l"_{"e"} = "r"_{"i"}*2*tan(pi/"N"_{"S"})`

Example

`"9.941125m"="12m"*2*tan(pi/"8")`

Calculator

LaTeX

Reset

👍

Download Regular Polygon Formulas PDF

Edge Length of Regular Polygon given Inradius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Edge Length of Regular Polygon = Inradius of Regular Polygon*2*tan(pi/Number of Sides of Regular Polygon)
l_e = r_i*2*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

Edge Length of Regular Polygon - (Measured in Meter) - The Edge Length of Regular Polygon is the length of one of the sides of the Regular Polygon.
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.
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.

STEP 1: Convert Input(s) to Base Unit

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

STEP 2: Evaluate Formula

Substituting Input Values in Formula

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

Evaluating ... ...

l_e = 9.94112549695428

STEP 3: Convert Result to Output's Unit

9.94112549695428 Meter --> No Conversion Required

FINAL ANSWER

9.94112549695428 ≈ 9.941125 Meter <-- Edge Length of Regular Polygon

(Calculation completed in 00.004 seconds)

You are here -

Home » Math » Geometry » Regular Polygon » 2D Geometry » Edge Length of Regular Polygon » Edge Length of Regular Polygon given Inradius

Credits

Created by Mona Gladys

St Joseph's College (SJC), Bengaluru

Mona Gladys has created this Calculator and 2000+ more calculators!

Verified by Nishan Poojary

Shri Madhwa Vadiraja Institute of Technology and Management (SMVITM), Udupi

Nishan Poojary has verified this Calculator and 400+ more calculators!

< 4 Edge Length of Regular Polygon Calculators

Edge Length of Regular Polygon given Area

Go Edge Length of Regular Polygon = sqrt(4*Area of Regular Polygon*tan(pi/Number of Sides of Regular Polygon))/sqrt(Number of Sides of Regular Polygon)

Edge Length of Regular Polygon given Circumradius

Go Edge Length of Regular Polygon = 2*Circumradius of Regular Polygon*sin(pi/Number of Sides of Regular Polygon)

Edge Length of Regular Polygon given Inradius

Go Edge Length of Regular Polygon = Inradius of Regular Polygon*2*tan(pi/Number of Sides of Regular Polygon)

Edge Length of Regular Polygon given Perimeter

Go Edge Length of Regular Polygon = Perimeter of Regular Polygon/Number of Sides of Regular Polygon

Edge Length of Regular Polygon given Inradius Formula

Edge Length of Regular Polygon = Inradius of Regular Polygon*2*tan(pi/Number of Sides of Regular Polygon)
l_e = r_i*2*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 Edge Length of Regular Polygon given Inradius?

Edge Length of Regular Polygon given Inradius calculator uses Edge Length of Regular Polygon = Inradius of Regular Polygon*2*tan(pi/Number of Sides of Regular Polygon) to calculate the Edge Length of Regular Polygon, The Edge Length of Regular Polygon given Inradius formula can be defined as the length of one of the sides of the Regular Polygon, calculated using its inradius. Edge Length of Regular Polygon is denoted by l_e symbol.

How to calculate Edge Length of Regular Polygon given Inradius using this online calculator? To use this online calculator for Edge Length of Regular Polygon given Inradius, enter Inradius of Regular Polygon (r_i) & Number of Sides of Regular Polygon (N_S) and hit the calculate button. Here is how the Edge Length of Regular Polygon given Inradius calculation can be explained with given input values -> 9.941125 = 12*2*tan(pi/8).

FAQ

What is Edge Length of Regular Polygon given Inradius?

The Edge Length of Regular Polygon given Inradius formula can be defined as the length of one of the sides of the Regular Polygon, calculated using its inradius and is represented as l_e = r_i*2*tan(pi/N_S) or Edge Length of Regular Polygon = Inradius of Regular Polygon*2*tan(pi/Number of Sides of Regular Polygon). 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 & 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.

How to calculate Edge Length of Regular Polygon given Inradius?

The Edge Length of Regular Polygon given Inradius formula can be defined as the length of one of the sides of the Regular Polygon, calculated using its inradius is calculated using Edge Length of Regular Polygon = Inradius of Regular Polygon*2*tan(pi/Number of Sides of Regular Polygon). To calculate Edge Length of Regular Polygon given Inradius, you need Inradius of Regular Polygon (r_i) & Number of Sides of Regular Polygon (N_S). With our tool, you need to enter the respective value for Inradius of Regular Polygon & Number of Sides 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 Edge Length of Regular Polygon?

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

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

Home

FREE PDFs

🔍 Search