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Inradius of Pentagon given Height Formula

GoInradius of Pentagon given Edge Length using Central Angle Formula

GoInradius of Pentagon given Circumradius using Central Angle 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{h}{\sqrt{5}}

r_i - Inradius of Pentagon?h - Height of Pentagon?

Inradius of Pentagon given Height Example

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Here is how the Inradius of Pentagon given Height equation looks like with Values.

Here is how the Inradius of Pentagon given Height equation looks like with Units.

Here is how the Inradius of Pentagon given Height equation looks like.

6.7082 = \frac{15}{\sqrt{5}}

6.7082m = \frac{15m}{\sqrt{5}}

6.7082 = \frac{15}{\sqrt{5}}

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Inradius of Pentagon given Height Solution

Follow our step by step solution on how to calculate Inradius of Pentagon given Height?

FIRST Step Consider the formula

r i = \frac{h}{\sqrt{5}}

Next Step Substitute values of Variables

∴

r i = \frac{15m}{\sqrt{5}}

Next Step Prepare to Evaluate

∴

r i = \frac{15}{\sqrt{5}}

Next Step Evaluate

∴

r i = 6.70820393249937m

LAST Step Rounding Answer

∴

r i = 6.7082m

Inradius of Pentagon given Height Formula Elements

Variables

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

Height of Pentagon

Height of Pentagon is the distance between one side of Pentagon and its opposite vertex.

Symbol: h

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Height of Pentagon

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

Other Formulas to find Inradius of Pentagon

Go Inradius of Pentagon given Edge Length using Central Angle

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

Go Inradius of Pentagon given Circumradius using Central Angle

r i = r c \cdot \cos (\frac{π}{5})

Go Inradius of Pentagon given Circumradius

r i = \frac{\sqrt{25 + (10 \cdot \sqrt{5})}}{\sqrt{50 + (10 \cdot \sqrt{5})}} \cdot r c

Go Inradius of Pentagon given Height using Central Angle

r i = \frac{h}{1 + (\frac{1}{\cos (\frac{π}{5})})}

How to Evaluate Inradius of Pentagon given Height?

Inradius of Pentagon given Height evaluator uses Inradius of Pentagon = Height of Pentagon/sqrt(5) to evaluate the Inradius of Pentagon, Inradius of Pentagon given Height is defined as the length of the line connecting the center and a point on the incircle of the Pentagon, calculated using height. Inradius of Pentagon is denoted by r_i symbol.

How to evaluate Inradius of Pentagon given Height using this online evaluator? To use this online evaluator for Inradius of Pentagon given Height, enter Height of Pentagon (h) and hit the calculate button.

FAQs on Inradius of Pentagon given Height

What is the formula to find Inradius of Pentagon given Height?

The formula of Inradius of Pentagon given Height is expressed as Inradius of Pentagon = Height of Pentagon/sqrt(5). Here is an example- 6.708204 = 15/sqrt(5).

How to calculate Inradius of Pentagon given Height?

With Height of Pentagon (h) we can find Inradius of Pentagon given Height using the formula - Inradius of Pentagon = Height of Pentagon/sqrt(5). This formula also uses Square Root Function 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)/(2*tan(pi/5))
Inradius of Pentagon=Circumradius of Pentagon*cos(pi/5)
Inradius of Pentagon=sqrt(25+(10*sqrt(5)))/sqrt(50+(10*sqrt(5)))*Circumradius of Pentagon

Can the Inradius of Pentagon given Height be negative?

No, the Inradius of Pentagon given Height, measured in Length cannot be negative.

Which unit is used to measure Inradius of Pentagon given Height?

Inradius of Pentagon given Height 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 Height can be measured.

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