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Inradius of Pentagon given Edge Length using Central 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{l e}{2 \cdot \tan (\frac{π}{5})}

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

Inradius of Pentagon given Edge Length using Central Angle Example

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

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

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

6.8819 = \frac{10}{2 \cdot \tan (\frac{3.1416}{5})}

6.8819m = \frac{10m}{2 \cdot \tan (\frac{3.1416}{5})}

6.8819 = \frac{10}{2 \cdot \tan (\frac{3.1416}{5})}

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Inradius of Pentagon given Edge Length using Central Angle Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

r i = \frac{10m}{2 \cdot \tan (\frac{π}{5})}

Next Step Substitute values of Constants

∴

r i = \frac{10m}{2 \cdot \tan (\frac{3.1416}{5})}

Next Step Prepare to Evaluate

∴

r i = \frac{10}{2 \cdot \tan (\frac{3.1416}{5})}

Next Step Evaluate

∴

r i = 6.88190960235587m

LAST Step Rounding Answer

∴

r i = 6.8819m

Inradius of Pentagon given Edge Length using Central 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

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 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 Interior Angle

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

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 Central Angle?

Inradius of Pentagon given Edge Length using Central Angle evaluator uses Inradius of Pentagon = (Edge Length of Pentagon)/(2*tan(pi/5)) to evaluate the Inradius of Pentagon, Inradius of Pentagon given Edge Length using Central 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 central angle. Inradius of Pentagon is denoted by r_i symbol.

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

FAQs on Inradius of Pentagon given Edge Length using Central Angle

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

The formula of Inradius of Pentagon given Edge Length using Central Angle is expressed as Inradius of Pentagon = (Edge Length of Pentagon)/(2*tan(pi/5)). Here is an example- 6.88191 = (10)/(2*tan(pi/5)).

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

With Edge Length of Pentagon (l_e) we can find Inradius of Pentagon given Edge Length using Central Angle using the formula - Inradius of Pentagon = (Edge Length of Pentagon)/(2*tan(pi/5)). This formula also uses Archimedes' constant and Tangent (tan) 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 Central Angle be negative?

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

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

Inradius of Pentagon given Edge Length using Central 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 Central Angle can be measured.

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