Edge Length of Pentagon given Inradius using Central Angle Calculator

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

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✖The Edge Length of Pentagon is the length of one of the five sides of the Pentagon.ⓘ Edge Length of Pentagon given Inradius using Central Angle [l_e]

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Edge Length of Pentagon given Inradius using Central Angle Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Edge Length of Pentagon - (Measured in Meter) - The Edge Length of Pentagon is the length of one of the five sides of the Pentagon.
Inradius of Pentagon - (Measured in Meter) - The Inradius of Pentagon is defined as the radius of the circle which is inscribed inside the Pentagon.

STEP 1: Convert Input(s) to Base Unit

Inradius of Pentagon: 7 Meter --> 7 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

l_e = 2*r_i*tan(pi/5) --> 2*7*tan(pi/5)

Evaluating ... ...

l_e = 10.1715953920751

STEP 3: Convert Result to Output's Unit

10.1715953920751 Meter --> No Conversion Required

FINAL ANSWER

10.1715953920751 ≈ 10.1716 Meter <-- Edge Length of Pentagon

(Calculation completed in 00.006 seconds)

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Created by Shweta Patil

Walchand College of Engineering (WCE), Sangli

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St Joseph's College (SJC), Bengaluru

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< Edge Length of Pentagon Calculators

Edge Length of Pentagon given Height using Central Angle

LaTeX Go Edge Length of Pentagon = (2*Height of Pentagon*sin(pi/5))/(1+cos(pi/5))

Edge Length of Pentagon given Area

LaTeX Go Edge Length of Pentagon = sqrt(4*Area of Pentagon/(sqrt(25+(10*sqrt(5)))))

Edge Length of Pentagon given Inradius

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

Edge Length of Pentagon given Area and Inradius

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

Edge Length of Pentagon given Inradius using Central Angle Formula

LaTeX Go

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

Edge Length of Pentagon given Inradius using Central Angle calculator uses Edge Length of Pentagon = 2*Inradius of Pentagon*tan(pi/5) to calculate the Edge Length of Pentagon, Edge Length of Pentagon given Inradius using Central Angle is defined as the length of the line connecting two adjacent vertices of the Pentagon, calculated using inradius and central angle. Edge Length of Pentagon is denoted by l_e symbol.

How to calculate Edge Length of Pentagon given Inradius using Central Angle using this online calculator? To use this online calculator for Edge Length of Pentagon given Inradius using Central Angle, enter Inradius of Pentagon (r_i) and hit the calculate button. Here is how the Edge Length of Pentagon given Inradius using Central Angle calculation can be explained with given input values -> 10.1716 = 2*7*tan(pi/5).

FAQ

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

Edge Length of Pentagon given Inradius using Central Angle is defined as the length of the line connecting two adjacent vertices of the Pentagon, calculated using inradius and central angle and is represented as l_e = 2*r_i*tan(pi/5) or Edge Length of Pentagon = 2*Inradius of Pentagon*tan(pi/5). The Inradius of Pentagon is defined as the radius of the circle which is inscribed inside the Pentagon.

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

Edge Length of Pentagon given Inradius using Central Angle is defined as the length of the line connecting two adjacent vertices of the Pentagon, calculated using inradius and central angle is calculated using Edge Length of Pentagon = 2*Inradius of Pentagon*tan(pi/5). To calculate Edge Length of Pentagon given Inradius using Central Angle, you need Inradius of Pentagon (r_i). With our tool, you need to enter the respective value for Inradius 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 Edge Length of Pentagon?

In this formula, Edge Length of Pentagon uses Inradius of Pentagon. We can use 3 other way(s) to calculate the same, which is/are as follows -

Edge Length of Pentagon = (2*Area of Pentagon)/(5*Inradius of Pentagon)
Edge Length of Pentagon = (2*Height of Pentagon*sin(pi/5))/(1+cos(pi/5))
Edge Length of Pentagon = Inradius of Pentagon*10/sqrt(25+(10*sqrt(5)))

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