Inradius of Pentagon given Edge Length using Interior Angle Calculator

✖The Inradius of Pentagon is defined as the radius of the circle which is inscribed inside the Pentagon.ⓘ Inradius of Pentagon given Edge Length using Interior Angle [r_i]

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Formula

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Inradius of Pentagon given Edge Length using Interior Angle

Formula

`"r"_{"i"} = ((1/2-cos(3/5*pi))^2*"l"_{"e"})/sin(3/5*pi)`

Example

`"6.88191m"=((1/2-cos(3/5*pi))^2*"10m")/sin(3/5*pi)`

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Inradius of Pentagon given Edge Length using Interior Angle Solution

STEP 0: Pre-Calculation Summary

Formula Used

Inradius of Pentagon = ((1/2-cos(3/5*pi))^2*Edge Length of Pentagon)/sin(3/5*pi)
r_i = ((1/2-cos(3/5*pi))^2*l_e)/sin(3/5*pi)
This formula uses 1 Constants, 2 Functions, 2 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

sin - Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse., sin(Angle)
cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., 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.
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 = ((1/2-cos(3/5*pi))^2*l_e)/sin(3/5*pi) --> ((1/2-cos(3/5*pi))^2*10)/sin(3/5*pi)

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 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 Edge Length using Interior Angle Formula

Inradius of Pentagon = ((1/2-cos(3/5*pi))^2*Edge Length of Pentagon)/sin(3/5*pi)
r_i = ((1/2-cos(3/5*pi))^2*l_e)/sin(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 Edge Length using Interior Angle?

Inradius of Pentagon given Edge Length using Interior Angle calculator uses Inradius of Pentagon = ((1/2-cos(3/5*pi))^2*Edge Length of Pentagon)/sin(3/5*pi) to calculate the Inradius of Pentagon, The Inradius of Pentagon given Edge Length 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 edge length and interior angle. Inradius of Pentagon is denoted by r_i symbol.

How to calculate Inradius of Pentagon given Edge Length using Interior Angle using this online calculator? To use this online calculator for Inradius of Pentagon given Edge Length using Interior Angle, enter Edge Length of Pentagon (l_e) and hit the calculate button. Here is how the Inradius of Pentagon given Edge Length using Interior Angle calculation can be explained with given input values -> 6.88191 = ((1/2-cos(3/5*pi))^2*10)/sin(3/5*pi).

FAQ

What is Inradius of Pentagon given Edge Length using Interior Angle?

The Inradius of Pentagon given Edge Length 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 edge length and interior angle and is represented as r_i = ((1/2-cos(3/5*pi))^2*l_e)/sin(3/5*pi) or Inradius of Pentagon = ((1/2-cos(3/5*pi))^2*Edge Length of Pentagon)/sin(3/5*pi). The Edge Length of Pentagon is the length of one of the five sides of the Pentagon.

How to calculate Inradius of Pentagon given Edge Length using Interior Angle?

The Inradius of Pentagon given Edge Length 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 edge length and interior angle is calculated using Inradius of Pentagon = ((1/2-cos(3/5*pi))^2*Edge Length of Pentagon)/sin(3/5*pi). To calculate Inradius of Pentagon given Edge Length using Interior Angle, 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 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 = Height of Pentagon-Circumradius of Pentagon
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 = Height of Pentagon-Circumradius of Pentagon
Inradius of Pentagon = (Edge Length of Pentagon)/(2*tan(pi/5))

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