Inradius of Pentagon given Circumradius using Interior Angle Solution

STEP 0: Pre-Calculation Summary
Formula Used
Inradius of Pentagon = Circumradius of Pentagon*(1/2-cos(3/5*pi))
ri = rc*(1/2-cos(3/5*pi))
This formula uses 1 Constants, 1 Functions, 2 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Functions Used
cos - Trigonometric cosine function, cos(Angle)
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.
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
Circumradius of Pentagon: 9 Meter --> 9 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
ri = rc*(1/2-cos(3/5*pi)) --> 9*(1/2-cos(3/5*pi))
Evaluating ... ...
ri = 7.28115294937453
STEP 3: Convert Result to Output's Unit
7.28115294937453 Meter --> No Conversion Required
FINAL ANSWER
7.28115294937453 7.281153 Meter <-- Inradius of Pentagon
(Calculation completed in 00.004 seconds)

Credits

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)

Inradius of Pentagon given Circumradius using Interior Angle Formula

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

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 using Interior Angle?

Inradius of Pentagon given Circumradius using Interior Angle calculator uses Inradius of Pentagon = Circumradius of Pentagon*(1/2-cos(3/5*pi)) to calculate the Inradius of Pentagon, The Inradius of Pentagon given Circumradius using Interior Angle is defined as the length of the line joining the center and a point on the incircle of the Pentagon, calculated using circumradius and interior angle. Inradius of Pentagon is denoted by ri symbol.

How to calculate Inradius of Pentagon given Circumradius using Interior Angle using this online calculator? To use this online calculator for Inradius of Pentagon given Circumradius using Interior Angle, enter Circumradius of Pentagon (rc) and hit the calculate button. Here is how the Inradius of Pentagon given Circumradius using Interior Angle calculation can be explained with given input values -> 7.281153 = 9*(1/2-cos(3/5*pi)).

FAQ

What is Inradius of Pentagon given Circumradius using Interior Angle?
The Inradius of Pentagon given Circumradius using Interior Angle is defined as the length of the line joining the center and a point on the incircle of the Pentagon, calculated using circumradius and interior angle and is represented as ri = rc*(1/2-cos(3/5*pi)) or Inradius of Pentagon = Circumradius of Pentagon*(1/2-cos(3/5*pi)). 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 using Interior Angle?
The Inradius of Pentagon given Circumradius using Interior Angle is defined as the length of the line joining the center and a point on the incircle of the Pentagon, calculated using circumradius and interior angle is calculated using Inradius of Pentagon = Circumradius of Pentagon*(1/2-cos(3/5*pi)). To calculate Inradius of Pentagon given Circumradius using Interior Angle, you need Circumradius of Pentagon (rc). With our tool, you need to enter the respective value for 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 Circumradius of Pentagon. We can use 16 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 = Height of Pentagon-Circumradius of Pentagon
  • Inradius of Pentagon = ((1/2-cos(3/5*pi))^2*Edge Length of Pentagon)/sin(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))))
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