Inradius of Pentagon given Circumradius and Height Calculator

✖Height of Pentagon is the distance between one side of Pentagon and its opposite vertex.ⓘ Height of Pentagon [h]			+10% -10%
✖The Circumradius of Pentagon is the radius of a circumcircle touching each of the vertices of Pentagon.ⓘ Circumradius of Pentagon [r_c]			+10% -10%

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

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Formula

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Inradius of Pentagon given Circumradius and Height

Formula

`"r"_{"i"} = "h"-"r"_{"c"}`

Example

`"6m"="15m"-"9m"`

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Inradius of Pentagon given Circumradius and Height Solution

STEP 0: Pre-Calculation Summary

Formula Used

Inradius of Pentagon = Height of Pentagon-Circumradius of Pentagon
r_i = h-r_c
This formula uses 3 Variables

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.
Height of Pentagon - (Measured in Meter) - Height of Pentagon is the distance between one side of Pentagon and its opposite vertex.
Circumradius of Pentagon - (Measured in Meter) - The Circumradius of Pentagon is the radius of a circumcircle touching each of the vertices of Pentagon.

STEP 1: Convert Input(s) to Base Unit

Height of Pentagon: 15 Meter --> 15 Meter No Conversion Required
Circumradius of Pentagon: 9 Meter --> 9 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

r_i = h-r_c --> 15-9

Evaluating ... ...

r_i = 6

STEP 3: Convert Result to Output's Unit

6 Meter --> No Conversion Required

FINAL ANSWER

6 Meter <-- Inradius of Pentagon

(Calculation completed in 00.004 seconds)

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Created by Dhruv Walia

Indian Institute of Technology, Indian School of Mines, DHANBAD (IIT ISM), Dhanbad, Jharkhand

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< 17 Inradius of Pentagon Calculators

Inradius of Pentagon given Area

Go Inradius of Pentagon = sqrt(25+(10*sqrt(5)))/10*sqrt(4*Area of Pentagon/sqrt(25+(10*sqrt(5))))

Inradius of Pentagon given Area using Interior Angle

Go Inradius of Pentagon = sqrt((2*Area of Pentagon*(1/2-cos(3/5*pi))^2)/(5*sin(3/5*pi)))

Inradius of Pentagon given Circumradius

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

Inradius of Pentagon given Edge Length using Interior Angle

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

Inradius of Pentagon given Diagonal

Go Inradius of Pentagon = sqrt(25+(10*sqrt(5)))*Diagonal of Pentagon/(5*(1+sqrt(5)))

Inradius of Pentagon given Width

Go Inradius of Pentagon = Width of Pentagon*sqrt(25+(10*sqrt(5)))/(5*(1+sqrt(5)))

Inradius of Pentagon given Area using Central Angle

Go Inradius of Pentagon = sqrt(Area of Pentagon/(5*tan(pi/5)))

Inradius of Pentagon

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

Inradius of Pentagon given Height using Interior Angle

Go Inradius of Pentagon = Height of Pentagon/(1+(1/(1/2-cos(3/5*pi))))

Inradius of Pentagon given Perimeter

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

Inradius of Pentagon given Circumradius using Interior Angle

Go Inradius of Pentagon = Circumradius of Pentagon*(1/2-cos(3/5*pi))

Inradius of Pentagon given Edge Length using Central Angle

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

Inradius of Pentagon given Height using Central Angle

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

Inradius of Pentagon given Circumradius using Central Angle

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

Inradius of Pentagon given Area and Edge Length

Go Inradius of Pentagon = (2*Area of Pentagon)/(5*Edge Length of Pentagon)

Inradius of Pentagon given Circumradius and Height

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

Inradius of Pentagon given Height

Go Inradius of Pentagon = Height of Pentagon/sqrt(5)

< 9 Radius of Pentagon Calculators

Circumradius of Pentagon given Edge Length using Interior Angle

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

Inradius of Pentagon given Edge Length using Interior Angle

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

Circumradius of Pentagon

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

Inradius of Pentagon

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

Circumradius of Pentagon given Edge Length using Central Angle

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

Inradius of Pentagon given Edge Length using Central Angle

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

Inradius of Pentagon given Area and Edge Length

Go Inradius of Pentagon = (2*Area of Pentagon)/(5*Edge Length of Pentagon)

Circumradius of Pentagon given Height and Inradius

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

Inradius of Pentagon given Circumradius and Height

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

Inradius of Pentagon given Circumradius and Height Formula

Inradius of Pentagon = Height of Pentagon-Circumradius of Pentagon
r_i = h-r_c

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 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 Circumradius and Height?

Inradius of Pentagon given Circumradius and Height calculator uses Inradius of Pentagon = Height of Pentagon-Circumradius of Pentagon to calculate the Inradius of Pentagon, The Inradius of Pentagon given Circumradius and Height is defined as the length of the line joining the center and a point on the incircle of the Pentagon, calculated using circumradius and height. Inradius of Pentagon is denoted by r_i symbol.

How to calculate Inradius of Pentagon given Circumradius and Height using this online calculator? To use this online calculator for Inradius of Pentagon given Circumradius and Height, enter Height of Pentagon (h) & Circumradius of Pentagon (r_c) and hit the calculate button. Here is how the Inradius of Pentagon given Circumradius and Height calculation can be explained with given input values -> 6 = 15-9.

FAQ

What is Inradius of Pentagon given Circumradius and Height?

The Inradius of Pentagon given Circumradius and Height is defined as the length of the line joining the center and a point on the incircle of the Pentagon, calculated using circumradius and height and is represented as r_i = h-r_c or Inradius of Pentagon = Height of Pentagon-Circumradius of Pentagon. Height of Pentagon is the distance between one side of Pentagon and its opposite vertex & The Circumradius of Pentagon is the radius of a circumcircle touching each of the vertices of Pentagon.

How to calculate Inradius of Pentagon given Circumradius and Height?

The Inradius of Pentagon given Circumradius and Height is defined as the length of the line joining the center and a point on the incircle of the Pentagon, calculated using circumradius and height is calculated using Inradius of Pentagon = Height of Pentagon-Circumradius of Pentagon. To calculate Inradius of Pentagon given Circumradius and Height, you need Height of Pentagon (h) & Circumradius of Pentagon (r_c). With our tool, you need to enter the respective value for Height of Pentagon & Circumradius 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 Height of Pentagon & Circumradius of Pentagon. We can use 20 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
Inradius of Pentagon = (Height of Pentagon)/(1+(1/cos(pi/5)))
Inradius of Pentagon = Height of Pentagon/sqrt(5)
Inradius of Pentagon = (2*Area of Pentagon)/(5*Edge Length of Pentagon)
Inradius of Pentagon = Edge Length of Pentagon/10*sqrt(25+(10*sqrt(5)))
Inradius of Pentagon = sqrt(25+(10*sqrt(5)))/10*sqrt(4*Area of Pentagon/sqrt(25+(10*sqrt(5))))
Inradius of Pentagon = Perimeter of Pentagon*sqrt(25+(10*sqrt(5)))/50
Inradius of Pentagon = Width of Pentagon*sqrt(25+(10*sqrt(5)))/(5*(1+sqrt(5)))
Inradius of Pentagon = sqrt(25+(10*sqrt(5)))*Diagonal of Pentagon/(5*(1+sqrt(5)))
Inradius of Pentagon = sqrt(Area of Pentagon/(5*tan(pi/5)))
Inradius of Pentagon = ((1/2-cos(3/5*pi))^2*Edge Length of Pentagon)/sin(3/5*pi)
Inradius of Pentagon = Circumradius of Pentagon*(1/2-cos(3/5*pi))
Inradius of Pentagon = sqrt((2*Area of Pentagon*(1/2-cos(3/5*pi))^2)/(5*sin(3/5*pi)))
Inradius of Pentagon = Height of Pentagon/(1+(1/(1/2-cos(3/5*pi))))
Inradius of Pentagon = Edge Length of Pentagon/10*sqrt(25+(10*sqrt(5)))
Inradius of Pentagon = (2*Area of Pentagon)/(5*Edge Length of Pentagon)
Inradius of Pentagon = (Edge Length of Pentagon)/(2*tan(pi/5))
Inradius of Pentagon = ((1/2-cos(3/5*pi))^2*Edge Length of Pentagon)/sin(3/5*pi)

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