Width 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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✖Width of Pentagon is the measurement or extent of horizontal distance from left to right of the Pentagon.ⓘ Width of Pentagon given Inradius [w]

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Width of Pentagon given Inradius Solution

STEP 0: Pre-Calculation Summary

Formula Used

Width of Pentagon = 5*Inradius of Pentagon*(1+sqrt(5))/sqrt(25+(10*sqrt(5)))
w = 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

Width of Pentagon - (Measured in Meter) - Width of Pentagon is the measurement or extent of horizontal distance from left to right 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

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

Evaluating ... ...

w = 16.4579870641892

STEP 3: Convert Result to Output's Unit

16.4579870641892 Meter --> No Conversion Required

FINAL ANSWER

16.4579870641892 ≈ 16.45799 Meter <-- Width of Pentagon

(Calculation completed in 00.004 seconds)

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< Width of Pentagon Calculators

Width of Pentagon given Area

LaTeX Go Width of Pentagon = (1+sqrt(5))/2*sqrt(4*Area of Pentagon/(sqrt(25+(10*sqrt(5)))))

Width of Pentagon given Circumradius

LaTeX Go Width of Pentagon = (1+sqrt(5))/2*(Circumradius of Pentagon*10/sqrt(50+(10*sqrt(5))))

Width of Pentagon

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

Width of Pentagon given Perimeter

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

Width of Pentagon given Inradius Formula

LaTeX Go

Width of Pentagon = 5*Inradius of Pentagon*(1+sqrt(5))/sqrt(25+(10*sqrt(5)))
w = 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 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 Width of Pentagon given Inradius?

Width of Pentagon given Inradius calculator uses Width of Pentagon = 5*Inradius of Pentagon*(1+sqrt(5))/sqrt(25+(10*sqrt(5))) to calculate the Width of Pentagon, The Width of Pentagon given Inradius formula is defined as the distance between non-adjacent vertices of the regular Pentagon(the length of its diagonal), calculated using inradius. Width of Pentagon is denoted by w symbol.

How to calculate Width of Pentagon given Inradius using this online calculator? To use this online calculator for Width of Pentagon given Inradius, enter Inradius of Pentagon (r_i) and hit the calculate button. Here is how the Width 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 Width of Pentagon given Inradius?

The Width of Pentagon given Inradius formula is defined as the distance between non-adjacent vertices of the regular Pentagon(the length of its diagonal), calculated using inradius and is represented as w = 5*r_i*(1+sqrt(5))/sqrt(25+(10*sqrt(5))) or Width 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 Width of Pentagon given Inradius?

The Width of Pentagon given Inradius formula is defined as the distance between non-adjacent vertices of the regular Pentagon(the length of its diagonal), calculated using inradius is calculated using Width of Pentagon = 5*Inradius of Pentagon*(1+sqrt(5))/sqrt(25+(10*sqrt(5))). To calculate Width 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 Width of Pentagon?

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

Width of Pentagon = (1+sqrt(5))/2*sqrt(4*Area of Pentagon/(sqrt(25+(10*sqrt(5)))))
Width of Pentagon = (1+sqrt(5))/2*Edge Length of Pentagon
Width of Pentagon = (1+sqrt(5))/2*(Circumradius of Pentagon*10/sqrt(50+(10*sqrt(5))))

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