Inradius of Pentagon Calculator

✖The Edge Length of Pentagon is the length of one of the five sides of the Pentagon.ⓘ Edge Length of Pentagon [l_e]

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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 [r_i]

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Inradius of Pentagon Solution

STEP 0: Pre-Calculation Summary

Formula Used

Inradius of Pentagon = Edge Length of Pentagon/10*sqrt(25+(10*sqrt(5)))
r_i = l_e/10*sqrt(25+(10*sqrt(5)))
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.
Edge Length of Pentagon - (Measured in Meter) - The Edge Length of Pentagon is the length of one of the five sides of the Pentagon.

STEP 1: Convert Input(s) to Base Unit

Edge Length of Pentagon: 10 Meter --> 10 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

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

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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Credits

Created by Shweta Patil

Walchand College of Engineering (WCE), Sangli

Shweta Patil has created this Calculator and 2500+ more calculators!

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St Joseph's College (SJC), Bengaluru

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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)

< Radius of Pentagon Calculators

Circumradius of Pentagon given Edge Length using Interior Angle

LaTeX Go Circumradius of Pentagon = (Edge Length of Pentagon*(1/2-cos(3/5*pi)))/(sin(3/5*pi))

Circumradius of Pentagon

LaTeX Go Circumradius of Pentagon = Edge Length of Pentagon/10*sqrt(50+(10*sqrt(5)))

Circumradius of Pentagon given Edge Length using Central Angle

LaTeX Go Circumradius of Pentagon = (Edge Length of Pentagon)/(2*sin(pi/5))

Circumradius of Pentagon given Height and Inradius

LaTeX Go Circumradius of Pentagon = Height of Pentagon-Inradius of Pentagon

Inradius of Pentagon Formula

LaTeX Go

Inradius of Pentagon = Edge Length of Pentagon/10*sqrt(25+(10*sqrt(5)))
r_i = l_e/10*sqrt(25+(10*sqrt(5)))

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?

Inradius of Pentagon calculator uses Inradius of Pentagon = Edge Length of Pentagon/10*sqrt(25+(10*sqrt(5))) to calculate the Inradius of Pentagon, Inradius of Pentagon is defined as the length of the line joining the center and a point on the incircle of Pentagon. Inradius of Pentagon is denoted by r_i symbol.

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

FAQ

What is Inradius of Pentagon?

Inradius of Pentagon is defined as the length of the line joining the center and a point on the incircle of Pentagon and is represented as r_i = l_e/10*sqrt(25+(10*sqrt(5))) or Inradius of Pentagon = Edge Length of Pentagon/10*sqrt(25+(10*sqrt(5))). The Edge Length of Pentagon is the length of one of the five sides of the Pentagon.

How to calculate Inradius of Pentagon?

Inradius of Pentagon is defined as the length of the line joining the center and a point on the incircle of Pentagon is calculated using Inradius of Pentagon = Edge Length of Pentagon/10*sqrt(25+(10*sqrt(5))). To calculate Inradius of Pentagon, you need Edge Length of Pentagon (l_e). With our tool, you need to enter the respective value for Edge Length 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 Edge Length 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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