Diagonal of Pentagon given Inradius 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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✖Diagonal of Pentagon is a straight line joining two non adjacent vertices of a Pentagon.ⓘ Diagonal of Pentagon given Inradius [d]

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Diagonal of Pentagon given Inradius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Diagonal of Pentagon = 5*Inradius of Pentagon*(1+sqrt(5))/sqrt(25+(10*sqrt(5)))
d = 5*r_i*(1+sqrt(5))/sqrt(25+(10*sqrt(5)))
This formula uses 1 Functions, 2 Variables

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Diagonal of Pentagon - (Measured in Meter) - Diagonal of Pentagon is a straight line joining two non adjacent vertices of a 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

d = 5*r_i*(1+sqrt(5))/sqrt(25+(10*sqrt(5))) --> 5*7*(1+sqrt(5))/sqrt(25+(10*sqrt(5)))

Evaluating ... ...

d = 16.4579870641892

STEP 3: Convert Result to Output's Unit

16.4579870641892 Meter --> No Conversion Required

FINAL ANSWER

16.4579870641892 ≈ 16.45799 Meter <-- Diagonal of Pentagon

(Calculation completed in 00.004 seconds)

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Created by Divanshi Jain

Netaji Subhash University of Technology, Delhi (NSUT Delhi), Dwarka

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< Diagonal of Pentagon Calculators

Diagonal of Pentagon given Area

LaTeX Go Diagonal of Pentagon = (1+sqrt(5))*sqrt(Area of Pentagon/sqrt(25+(10*sqrt(5))))

Diagonal of Pentagon given Circumradius

LaTeX Go Diagonal of Pentagon = Circumradius of Pentagon/(sqrt((5-sqrt(5))/10))

Diagonal of Pentagon

LaTeX Go Diagonal of Pentagon = (1+sqrt(5))*Edge Length of Pentagon/2

Diagonal of Pentagon given Perimeter

LaTeX Go Diagonal of Pentagon = (1+sqrt(5))*Perimeter of Pentagon/10

Diagonal of Pentagon given Inradius Formula

LaTeX Go

Diagonal of Pentagon = 5*Inradius of Pentagon*(1+sqrt(5))/sqrt(25+(10*sqrt(5)))
d = 5*r_i*(1+sqrt(5))/sqrt(25+(10*sqrt(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 is 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 Diagonal of Pentagon given Inradius?

Diagonal of Pentagon given Inradius calculator uses Diagonal of Pentagon = 5*Inradius of Pentagon*(1+sqrt(5))/sqrt(25+(10*sqrt(5))) to calculate the Diagonal of Pentagon, The Diagonal of Pentagon given Inradius formula is defined as the length of the line segment joining two non adjacent vertices of Pentagon, calculated using inradius. Diagonal of Pentagon is denoted by d symbol.

How to calculate Diagonal of Pentagon given Inradius using this online calculator? To use this online calculator for Diagonal of Pentagon given Inradius, enter Inradius of Pentagon (r_i) and hit the calculate button. Here is how the Diagonal of Pentagon given Inradius calculation can be explained with given input values -> 16.45799 = 5*7*(1+sqrt(5))/sqrt(25+(10*sqrt(5))).

FAQ

What is Diagonal of Pentagon given Inradius?

The Diagonal of Pentagon given Inradius formula is defined as the length of the line segment joining two non adjacent vertices of Pentagon, calculated using inradius and is represented as d = 5*r_i*(1+sqrt(5))/sqrt(25+(10*sqrt(5))) or Diagonal of Pentagon = 5*Inradius of Pentagon*(1+sqrt(5))/sqrt(25+(10*sqrt(5))). The Inradius of Pentagon is defined as the radius of the circle which is inscribed inside the Pentagon.

How to calculate Diagonal of Pentagon given Inradius?

The Diagonal of Pentagon given Inradius formula is defined as the length of the line segment joining two non adjacent vertices of Pentagon, calculated using inradius is calculated using Diagonal of Pentagon = 5*Inradius of Pentagon*(1+sqrt(5))/sqrt(25+(10*sqrt(5))). To calculate Diagonal of Pentagon given Inradius, 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 Diagonal of Pentagon?

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

Diagonal of Pentagon = Circumradius of Pentagon/(sqrt((5-sqrt(5))/10))
Diagonal of Pentagon = (1+sqrt(5))*Edge Length of Pentagon/2
Diagonal of Pentagon = (1+sqrt(5))*sqrt(Area of Pentagon/sqrt(25+(10*sqrt(5))))

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