Inradius of Pentagon given Edge Length using Central Angle 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 given Edge Length using Central Angle [r_i]

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Inradius of Pentagon given Edge Length using Central Angle Solution

STEP 0: Pre-Calculation Summary

Formula Used

Inradius of Pentagon = (Edge Length of Pentagon)/(2*tan(pi/5))
r_i = (l_e)/(2*tan(pi/5))
This formula uses 1 Constants, 1 Functions, 2 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

tan - The tangent of an angle is a trigonometric ratio of the length of the side opposite an angle to the length of the side adjacent to an angle in a right triangle., tan(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 = (l_e)/(2*tan(pi/5)) --> (10)/(2*tan(pi/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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Created by Shweta Patil

Walchand College of Engineering (WCE), Sangli

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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 given Edge Length using Central Angle Formula

LaTeX Go

Inradius of Pentagon = (Edge Length of Pentagon)/(2*tan(pi/5))
r_i = (l_e)/(2*tan(pi/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 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 Central Angle?

Inradius of Pentagon given Edge Length using Central Angle calculator uses Inradius of Pentagon = (Edge Length of Pentagon)/(2*tan(pi/5)) to calculate the Inradius of Pentagon, Inradius of Pentagon given Edge Length using Central 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 central angle. Inradius of Pentagon is denoted by r_i symbol.

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

FAQ

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

Inradius of Pentagon given Edge Length using Central 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 central angle and is represented as r_i = (l_e)/(2*tan(pi/5)) or Inradius of Pentagon = (Edge Length of Pentagon)/(2*tan(pi/5)). 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 Central Angle?

Inradius of Pentagon given Edge Length using Central 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 central angle is calculated using Inradius of Pentagon = (Edge Length of Pentagon)/(2*tan(pi/5)). To calculate Inradius of Pentagon given Edge Length using Central 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 3 other way(s) to calculate the same, which is/are as follows -

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)))

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