Inradius of Pentagon given Perimeter Calculator

✖The Perimeter of Pentagon is the total distance around the edge of the Pentagon.ⓘ Perimeter of Pentagon [P]

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✖The Inradius of Pentagon is defined as the radius of the circle which is inscribed inside the Pentagon.ⓘ Inradius of Pentagon given Perimeter [r_i]

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Inradius of Pentagon given Perimeter Solution

STEP 0: Pre-Calculation Summary

Formula Used

Inradius of Pentagon = Perimeter of Pentagon*sqrt(25+(10*sqrt(5)))/50
r_i = P*sqrt(25+(10*sqrt(5)))/50
This formula uses 1 Functions, 2 Variables

Functions Used

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., sqrt(Number)

Variables Used

Inradius of Pentagon - (Measured in Meter) - The Inradius of Pentagon is defined as the radius of the circle which is inscribed inside the Pentagon.
Perimeter of Pentagon - (Measured in Meter) - The Perimeter of Pentagon is the total distance around the edge of the Pentagon.

STEP 1: Convert Input(s) to Base Unit

Perimeter of Pentagon: 50 Meter --> 50 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_i = P*sqrt(25+(10*sqrt(5)))/50 --> 50*sqrt(25+(10*sqrt(5)))/50

Evaluating ... ...

r_i = 6.88190960235587

STEP 3: Convert Result to Output's Unit

6.88190960235587 Meter --> No Conversion Required

FINAL ANSWER

6.88190960235587 ≈ 6.88191 Meter <-- Inradius of Pentagon

(Calculation completed in 00.004 seconds)

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Created by Divanshi Jain

Netaji Subhash University of Technology, Delhi (NSUT Delhi), Dwarka

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< Inradius of Pentagon Calculators

Inradius of Pentagon given Circumradius

LaTeX Go Inradius of Pentagon = sqrt(25+(10*sqrt(5)))/sqrt(50+(10*sqrt(5)))*Circumradius of Pentagon

Inradius of Pentagon given Edge Length using Central Angle

LaTeX Go Inradius of Pentagon = (Edge Length of Pentagon)/(2*tan(pi/5))

Inradius of Pentagon given Height using Central Angle

LaTeX Go Inradius of Pentagon = (Height of Pentagon)/(1+(1/cos(pi/5)))

Inradius of Pentagon given Circumradius using Central Angle

LaTeX Go Inradius of Pentagon = Circumradius of Pentagon*cos(pi/5)

Inradius of Pentagon given Perimeter Formula

LaTeX Go

Inradius of Pentagon = Perimeter of Pentagon*sqrt(25+(10*sqrt(5)))/50
r_i = P*sqrt(25+(10*sqrt(5)))/50

What is Pentagon?

A Pentagon shape is a flat shape or a flat (two-dimensional) 5-sided geometric shape. In geometry, it is considered as a is a five-sided polygon with five straight sides and five interior angles, which add up to 540°. Pentagons can be simple or self-intersecting. A simple pentagon (5-gon) must have five straight sides that meet to create five vertices but do not intersect with each other. A self-intersecting regular pentagon is called a pentagram.

How to Calculate Inradius of Pentagon given Perimeter?

Inradius of Pentagon given Perimeter calculator uses Inradius of Pentagon = Perimeter of Pentagon*sqrt(25+(10*sqrt(5)))/50 to calculate 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 calculate Inradius of Pentagon given Perimeter using this online calculator? To use this online calculator for Inradius of Pentagon given Perimeter, enter Perimeter of Pentagon (P) and hit the calculate button. Here is how the Inradius of Pentagon given Perimeter calculation can be explained with given input values -> 6.88191 = 50*sqrt(25+(10*sqrt(5)))/50.

FAQ

What is Inradius of Pentagon given Perimeter?

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 and is represented as r_i = P*sqrt(25+(10*sqrt(5)))/50 or Inradius of Pentagon = Perimeter of Pentagon*sqrt(25+(10*sqrt(5)))/50. The Perimeter of Pentagon is the total distance around the edge of the Pentagon.

How to calculate Inradius of Pentagon given Perimeter?

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 is calculated using Inradius of Pentagon = Perimeter of Pentagon*sqrt(25+(10*sqrt(5)))/50. To calculate Inradius of Pentagon given Perimeter, you need Perimeter of Pentagon (P). With our tool, you need to enter the respective value for Perimeter of Pentagon and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Inradius of Pentagon?

In this formula, Inradius of Pentagon uses Perimeter of Pentagon. We can use 3 other way(s) to calculate the same, which is/are as follows -

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

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