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Inradius of Pentagon given Edge Length using Interior Angle Formula

GoInradius of Pentagon Formula

GoInradius of Pentagon given Area and Edge Length Formula

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The Inradius of Pentagon is defined as the radius of the circle which is inscribed inside the Pentagon. Check FAQs

r i = \frac{{(\frac{1}{2} - \cos (\frac{3}{5} \cdot π))}^{2} \cdot l e}{\sin (\frac{3}{5} \cdot π)}

r_i - Inradius of Pentagon?l_e - Edge Length of Pentagon?π - Archimedes' constant?

Inradius of Pentagon given Edge Length using Interior Angle Example

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Here is how the Inradius of Pentagon given Edge Length using Interior Angle equation looks like with Values.

Here is how the Inradius of Pentagon given Edge Length using Interior Angle equation looks like with Units.

Here is how the Inradius of Pentagon given Edge Length using Interior Angle equation looks like.

6.8819 = \frac{{(\frac{1}{2} - \cos (\frac{3}{5} \cdot 3.1416))}^{2} \cdot 10}{\sin (\frac{3}{5} \cdot 3.1416)}

6.8819m = \frac{{(\frac{1}{2} - \cos (\frac{3}{5} \cdot 3.1416))}^{2} \cdot 10m}{\sin (\frac{3}{5} \cdot 3.1416)}

6.8819 = \frac{{(\frac{1}{2} - \cos (\frac{3}{5} \cdot 3.1416))}^{2} \cdot 10}{\sin (\frac{3}{5} \cdot 3.1416)}

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Inradius of Pentagon given Edge Length using Interior Angle Solution

Follow our step by step solution on how to calculate Inradius of Pentagon given Edge Length using Interior Angle?

FIRST Step Consider the formula

r i = \frac{{(\frac{1}{2} - \cos (\frac{3}{5} \cdot π))}^{2} \cdot l e}{\sin (\frac{3}{5} \cdot π)}

Next Step Substitute values of Variables

∴

r i = \frac{{(\frac{1}{2} - \cos (\frac{3}{5} \cdot π))}^{2} \cdot 10m}{\sin (\frac{3}{5} \cdot π)}

Next Step Substitute values of Constants

∴

r i = \frac{{(\frac{1}{2} - \cos (\frac{3}{5} \cdot 3.1416))}^{2} \cdot 10m}{\sin (\frac{3}{5} \cdot 3.1416)}

Next Step Prepare to Evaluate

∴

r i = \frac{{(\frac{1}{2} - \cos (\frac{3}{5} \cdot 3.1416))}^{2} \cdot 10}{\sin (\frac{3}{5} \cdot 3.1416)}

Next Step Evaluate

∴

r i = 6.88190960235587m

LAST Step Rounding Answer

∴

r i = 6.8819m

Inradius of Pentagon given Edge Length using Interior Angle Formula Elements

Variables

Constants

Functions

Inradius of Pentagon

The Inradius of Pentagon is defined as the radius of the circle which is inscribed inside the Pentagon.

Symbol: r_i

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Inradius of Pentagon

Edge Length of Pentagon

The Edge Length of Pentagon is the length of one of the five sides of the Pentagon.

Symbol: l_e

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Edge Length of Pentagon

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

sin

Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse.

Syntax: sin(Angle)

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: cos(Angle)

Other Formulas to find Inradius of Pentagon

Go Inradius of Pentagon

r i = \frac{l e}{10} \cdot \sqrt{25 + (10 \cdot \sqrt{5})}

Go Inradius of Pentagon given Area and Edge Length

r i = \frac{2 \cdot A}{5 \cdot l e}

Go Inradius of Pentagon given Circumradius and Height

r i = h - r c

Go Inradius of Pentagon given Edge Length using Central Angle

r i = \frac{l e}{2 \cdot \tan (\frac{π}{5})}

Other formulas in Inradius of Pentagon category

Go Circumradius of Pentagon

r c = \frac{l e}{10} \cdot \sqrt{50 + (10 \cdot \sqrt{5})}

Go Circumradius of Pentagon given Edge Length using Central Angle

r c = \frac{l e}{2 \cdot \sin (\frac{π}{5})}

Go Circumradius of Pentagon given Edge Length using Interior Angle

r c = \frac{l e \cdot (\frac{1}{2} - \cos (\frac{3}{5} \cdot π))}{\sin (\frac{3}{5} \cdot π)}

Go Circumradius of Pentagon given Height and Inradius

r c = h - r i

How to Evaluate Inradius of Pentagon given Edge Length using Interior Angle?

Inradius of Pentagon given Edge Length using Interior Angle evaluator uses Inradius of Pentagon = ((1/2-cos(3/5*pi))^2*Edge Length of Pentagon)/sin(3/5*pi) to evaluate the Inradius of Pentagon, The Inradius of Pentagon given Edge Length using Interior Angle is defined as the length of the line joining the center and a point on the incircle of the Pentagon, calculated using edge length and interior angle. Inradius of Pentagon is denoted by r_i symbol.

How to evaluate Inradius of Pentagon given Edge Length using Interior Angle using this online evaluator? To use this online evaluator for Inradius of Pentagon given Edge Length using Interior Angle, enter Edge Length of Pentagon (l_e) and hit the calculate button.

FAQs on Inradius of Pentagon given Edge Length using Interior Angle

What is the formula to find Inradius of Pentagon given Edge Length using Interior Angle?

The formula of Inradius of Pentagon given Edge Length using Interior Angle is expressed as Inradius of Pentagon = ((1/2-cos(3/5*pi))^2*Edge Length of Pentagon)/sin(3/5*pi). Here is an example- 6.88191 = ((1/2-cos(3/5*pi))^2*10)/sin(3/5*pi).

How to calculate Inradius of Pentagon given Edge Length using Interior Angle?

With Edge Length of Pentagon (l_e) we can find Inradius of Pentagon given Edge Length using Interior Angle using the formula - Inradius of Pentagon = ((1/2-cos(3/5*pi))^2*Edge Length of Pentagon)/sin(3/5*pi). This formula also uses Archimedes' constant and , Sine, Cosine function(s).

What are the other ways to Calculate Inradius of Pentagon?

Here are the different ways to Calculate Inradius of Pentagon-

Inradius of Pentagon=Edge Length of Pentagon/10*sqrt(25+(10*sqrt(5)))
Inradius of Pentagon=(2*Area of Pentagon)/(5*Edge Length of Pentagon)
Inradius of Pentagon=Height of Pentagon-Circumradius of Pentagon

Can the Inradius of Pentagon given Edge Length using Interior Angle be negative?

No, the Inradius of Pentagon given Edge Length using Interior Angle, measured in Length cannot be negative.

Which unit is used to measure Inradius of Pentagon given Edge Length using Interior Angle?

Inradius of Pentagon given Edge Length using Interior Angle is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Inradius of Pentagon given Edge Length using Interior Angle can be measured.

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