## Inradius of Pentagon given Height using Interior Angle Solution

STEP 0: Pre-Calculation Summary
Formula Used
Inradius of Pentagon = Height of Pentagon/(1+(1/(1/2-cos(3/5*pi))))
ri = h/(1+(1/(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.
Height of Pentagon - (Measured in Meter) - Height of Pentagon is the distance between one side of Pentagon and its opposite vertex.
STEP 1: Convert Input(s) to Base Unit
Height of Pentagon: 15 Meter --> 15 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
ri = h/(1+(1/(1/2-cos(3/5*pi)))) --> 15/(1+(1/(1/2-cos(3/5*pi))))
Evaluating ... ...
ri = 6.70820393249937
STEP 3: Convert Result to Output's Unit
6.70820393249937 Meter --> No Conversion Required
6.70820393249937 6.708204 Meter <-- Inradius of Pentagon
(Calculation completed in 00.003 seconds)
You are here -
Home » Math »

## Credits

Created by Dhruv Walia
Indian Institute of Technology, Indian School of Mines, DHANBAD (IIT ISM), Dhanbad, Jharkhand
Dhruv Walia has created this Calculator and 700+ more calculators!
Verified by Nikhil
Mumbai University (DJSCE), Mumbai
Nikhil has verified this Calculator and 200+ more calculators!

## < 17 Inradius of Pentagon Calculators

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
Inradius of Pentagon = sqrt((2*Area of Pentagon*(1/2-cos(3/5*pi))^2)/(5*sin(3/5*pi)))
Inradius of Pentagon given Edge Length using Interior Angle
Inradius of Pentagon = ((1/2-cos(3/5*pi))^2*Edge Length of Pentagon)/sin(3/5*pi)
Inradius of Pentagon = sqrt(25+(10*sqrt(5)))*Diagonal of Pentagon/(5*(1+sqrt(5)))
Inradius of Pentagon = Width of Pentagon*sqrt(25+(10*sqrt(5)))/(5*(1+sqrt(5)))
Inradius of Pentagon given Area using Central Angle
Inradius of Pentagon = sqrt(Area of Pentagon/(5*tan(pi/5)))
Inradius of Pentagon = Edge Length of Pentagon/10*sqrt(25+(10*sqrt(5)))
Inradius of Pentagon given Height using Interior Angle
Inradius of Pentagon = Height of Pentagon/(1+(1/(1/2-cos(3/5*pi))))
Inradius of Pentagon = Perimeter of Pentagon*sqrt(25+(10*sqrt(5)))/50
Inradius of Pentagon given Edge Length using Central Angle
Inradius of Pentagon = (Edge Length of Pentagon)/(2*tan(pi/5))
Inradius of Pentagon given Height using Central Angle
Inradius of Pentagon = (Height of Pentagon)/(1+(1/cos(pi/5)))
Inradius of Pentagon given Area and Edge Length
Inradius of Pentagon = (2*Area of Pentagon)/(5*Edge Length of Pentagon)
Inradius of Pentagon = Height of Pentagon/sqrt(5)

## Inradius of Pentagon given Height using Interior Angle Formula

Inradius of Pentagon = Height of Pentagon/(1+(1/(1/2-cos(3/5*pi))))
ri = h/(1+(1/(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 Height using Interior Angle?

Inradius of Pentagon given Height using Interior Angle calculator uses Inradius of Pentagon = Height of Pentagon/(1+(1/(1/2-cos(3/5*pi)))) to calculate the Inradius of Pentagon, The Inradius of Pentagon given Height 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 height and interior angle. Inradius of Pentagon is denoted by ri symbol.

How to calculate Inradius of Pentagon given Height using Interior Angle using this online calculator? To use this online calculator for Inradius of Pentagon given Height using Interior Angle, enter Height of Pentagon (h) and hit the calculate button. Here is how the Inradius of Pentagon given Height using Interior Angle calculation can be explained with given input values -> 6.708204 = 15/(1+(1/(1/2-cos(3/5*pi)))).

### FAQ

What is Inradius of Pentagon given Height using Interior Angle?
The Inradius of Pentagon given Height 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 height and interior angle and is represented as ri = h/(1+(1/(1/2-cos(3/5*pi)))) or Inradius of Pentagon = Height of Pentagon/(1+(1/(1/2-cos(3/5*pi)))). Height of Pentagon is the distance between one side of Pentagon and its opposite vertex.
How to calculate Inradius of Pentagon given Height using Interior Angle?
The Inradius of Pentagon given Height 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 height and interior angle is calculated using Inradius of Pentagon = Height of Pentagon/(1+(1/(1/2-cos(3/5*pi)))). To calculate Inradius of Pentagon given Height using Interior Angle, you need Height of Pentagon (h). With our tool, you need to enter the respective value for Height 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. 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 = (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))) 