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Edge Length of Pentagon given Inradius Formula

GoEdge Length of Pentagon given Area and Inradius Formula

GoEdge Length of Pentagon given Height using Central Angle Formula

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

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

l_e - Edge Length of Pentagon?r_i - Inradius of Pentagon?

Edge Length of Pentagon given Inradius Example

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

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

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

10.1716 = 7 \cdot \frac{10}{\sqrt{25 + (10 \cdot \sqrt{5})}}

10.1716m = 7m \cdot \frac{10}{\sqrt{25 + (10 \cdot \sqrt{5})}}

10.1716 = 7 \cdot \frac{10}{\sqrt{25 + (10 \cdot \sqrt{5})}}

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Edge Length of Pentagon given Inradius Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

l e = 7m \cdot \frac{10}{\sqrt{25 + (10 \cdot \sqrt{5})}}

Next Step Prepare to Evaluate

∴

l e = 7 \cdot \frac{10}{\sqrt{25 + (10 \cdot \sqrt{5})}}

Next Step Evaluate

∴

l e = 10.1715953920751m

LAST Step Rounding Answer

∴

l e = 10.1716m

Edge Length of Pentagon given Inradius Formula Elements

Variables

Functions

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

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

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 Edge Length of Pentagon

Go Edge Length of Pentagon given Area and Inradius

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

Go Edge Length of Pentagon given Height using Central Angle

l e = \frac{2 \cdot h \cdot \sin (\frac{π}{5})}{1 + \cos (\frac{π}{5})}

Go Edge Length of Pentagon given Area

l e = \sqrt{4 \cdot \frac{A}{\sqrt{25 + (10 \cdot \sqrt{5})}}}

Go Edge Length of Pentagon given Height

l e = h \cdot \frac{2}{\sqrt{5 + (2 \cdot \sqrt{5})}}

How to Evaluate Edge Length of Pentagon given Inradius?

Edge Length of Pentagon given Inradius evaluator uses Edge Length of Pentagon = Inradius of Pentagon*10/sqrt(25+(10*sqrt(5))) to evaluate the Edge Length of Pentagon, Edge Length of Pentagon given Inradius is defined as the length of the line connecting the two adjacent vertices of the Pentagon, calculated using inradius. Edge Length of Pentagon is denoted by l_e symbol.

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

FAQs on Edge Length of Pentagon given Inradius

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

The formula of Edge Length of Pentagon given Inradius is expressed as Edge Length of Pentagon = Inradius of Pentagon*10/sqrt(25+(10*sqrt(5))). Here is an example- 10.1716 = 7*10/sqrt(25+(10*sqrt(5))).

How to calculate Edge Length of Pentagon given Inradius?

With Inradius of Pentagon (r_i) we can find Edge Length of Pentagon given Inradius using the formula - Edge Length of Pentagon = Inradius of Pentagon*10/sqrt(25+(10*sqrt(5))). This formula also uses Square Root Function function(s).

What are the other ways to Calculate Edge Length of Pentagon?

Here are the different ways to Calculate Edge Length of Pentagon-

Edge Length of Pentagon=(2*Area of Pentagon)/(5*Inradius of Pentagon)
Edge Length of Pentagon=(2*Height of Pentagon*sin(pi/5))/(1+cos(pi/5))
Edge Length of Pentagon=sqrt(4*Area of Pentagon/(sqrt(25+(10*sqrt(5)))))

Can the Edge Length of Pentagon given Inradius be negative?

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

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

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

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