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Inradius of Pentagon given Perimeter 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 = P \cdot \frac{\sqrt{25 + (10 \cdot \sqrt{5})}}{50}

r_i - Inradius of Pentagon?P - Perimeter of Pentagon?

Inradius of Pentagon given Perimeter Example

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

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

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

6.8819 = 50 \cdot \frac{\sqrt{25 + (10 \cdot \sqrt{5})}}{50}

6.8819m = 50m \cdot \frac{\sqrt{25 + (10 \cdot \sqrt{5})}}{50}

6.8819 = 50 \cdot \frac{\sqrt{25 + (10 \cdot \sqrt{5})}}{50}

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Inradius of Pentagon given Perimeter Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

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

Next Step Prepare to Evaluate

∴

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

Next Step Evaluate

∴

r i = 6.88190960235587m

LAST Step Rounding Answer

∴

r i = 6.8819m

Inradius of Pentagon given Perimeter 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

Perimeter of Pentagon

The Perimeter of Pentagon is the total distance around the edge of the Pentagon.

Symbol: P

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Perimeter 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 Perimeter?

Inradius of Pentagon given Perimeter evaluator uses Inradius of Pentagon = Perimeter of Pentagon*sqrt(25+(10*sqrt(5)))/50 to evaluate the Inradius of Pentagon, The Inradius of Pentagon given Perimeter formula is defined as the length of the line joining the center and a point on the incircle of Pentagon, calculated using perimeter of Pentagon. Inradius of Pentagon is denoted by r_i symbol.

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

FAQs on Inradius of Pentagon given Perimeter

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

The formula of Inradius of Pentagon given Perimeter is expressed as Inradius of Pentagon = Perimeter of Pentagon*sqrt(25+(10*sqrt(5)))/50. Here is an example- 6.88191 = 50*sqrt(25+(10*sqrt(5)))/50.

How to calculate Inradius of Pentagon given Perimeter?

With Perimeter of Pentagon (P) we can find Inradius of Pentagon given Perimeter using the formula - Inradius of Pentagon = Perimeter of Pentagon*sqrt(25+(10*sqrt(5)))/50. This formula also uses Square Root (sqrt) 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 Perimeter be negative?

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

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

Inradius of Pentagon given Perimeter 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 Perimeter can be measured.

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