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Inradius of N-gon Formula

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Inradius of N-gon is defined as the radius of the circle which is inscribed inside the N-gon. Check FAQs

r i = \frac{l e}{2 \cdot \tan (\frac{π}{N Sides})}

r_i - Inradius of N-gon?l_e - Edge Length of N-gon?N_Sides - Number of Sides of N-gon?π - Archimedes' constant?

Inradius of N-gon Example

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Here is how the Inradius of N-gon equation looks like with Values.

Here is how the Inradius of N-gon equation looks like with Units.

Here is how the Inradius of N-gon equation looks like.

12.0711 = \frac{10}{2 \cdot \tan (\frac{3.1416}{8})}

12.0711m = \frac{10m}{2 \cdot \tan (\frac{3.1416}{8})}

12.0711 = \frac{10}{2 \cdot \tan (\frac{3.1416}{8})}

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Inradius of N-gon Solution

Follow our step by step solution on how to calculate Inradius of N-gon?

FIRST Step Consider the formula

r i = \frac{l e}{2 \cdot \tan (\frac{π}{N Sides})}

Next Step Substitute values of Variables

∴

r i = \frac{10m}{2 \cdot \tan (\frac{π}{8})}

Next Step Substitute values of Constants

∴

r i = \frac{10m}{2 \cdot \tan (\frac{3.1416}{8})}

Next Step Prepare to Evaluate

∴

r i = \frac{10}{2 \cdot \tan (\frac{3.1416}{8})}

Next Step Evaluate

∴

r i = 12.0710678118655m

LAST Step Rounding Answer

∴

r i = 12.0711m

Inradius of N-gon Formula Elements

Variables

Constants

Functions

Inradius of N-gon

Inradius of N-gon is defined as the radius of the circle which is inscribed inside the N-gon.

Symbol: r_i

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Inradius of N-gon

Edge Length of N-gon

Edge Length of N-gon is the length of the line segment joining two adjacent vertices of N-gon.

Symbol: l_e

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Edge Length of N-gon

Number of Sides of N-gon

Number of Sides of N-gon is the number of line segments required to make a N-gon.

Symbol: N_Sides

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Number of Sides of N-gon

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

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.

Syntax: tan(Angle)

Other formulas in Radius of N gon category

Go Circumradius of N-gon

r c = \frac{l e}{2 \cdot \sin (\frac{π}{N Sides})}

How to Evaluate Inradius of N-gon?

Inradius of N-gon evaluator uses Inradius of N-gon = Edge Length of N-gon/(2*tan(pi/Number of Sides of N-gon)) to evaluate the Inradius of N-gon, The Inradius of N-gon formula is defined as the radius of the circle which is inscribed inside the N-gon. Inradius of N-gon is denoted by r_i symbol.

How to evaluate Inradius of N-gon using this online evaluator? To use this online evaluator for Inradius of N-gon, enter Edge Length of N-gon (l_e) & Number of Sides of N-gon (N_Sides) and hit the calculate button.

FAQs on Inradius of N-gon

What is the formula to find Inradius of N-gon?

The formula of Inradius of N-gon is expressed as Inradius of N-gon = Edge Length of N-gon/(2*tan(pi/Number of Sides of N-gon)). Here is an example- 12.07107 = 10/(2*tan(pi/8)).

How to calculate Inradius of N-gon?

With Edge Length of N-gon (l_e) & Number of Sides of N-gon (N_Sides) we can find Inradius of N-gon using the formula - Inradius of N-gon = Edge Length of N-gon/(2*tan(pi/Number of Sides of N-gon)). This formula also uses Archimedes' constant and Tangent (tan) function(s).

Can the Inradius of N-gon be negative?

No, the Inradius of N-gon, measured in Length cannot be negative.

Which unit is used to measure Inradius of N-gon?

Inradius of N-gon is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Inradius of N-gon can be measured.

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Inradius of N-gon Formula

Inradius of N-gon Example

Inradius of N-gon Solution

Inradius of N-gon Formula Elements

Other formulas in Radius of N gon category

How to Evaluate Inradius of N-gon?

FAQs on Inradius of N-gon

Variable Name