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Width of Pentagon given Inradius Formula

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GoWidth of Pentagon Formula

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Width of Pentagon is the measurement or extent of horizontal distance from left to right of the Pentagon. Check FAQs

w = 5 \cdot r i \cdot \frac{1 + \sqrt{5}}{\sqrt{25 + (10 \cdot \sqrt{5})}}

w - Width of Pentagon?r_i - Inradius of Pentagon?

Width of Pentagon given Inradius Example

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Here is how the Width of Pentagon given Inradius equation looks like with Values.

Here is how the Width of Pentagon given Inradius equation looks like with Units.

Here is how the Width of Pentagon given Inradius equation looks like.

16.458 = 5 \cdot 7 \cdot \frac{1 + \sqrt{5}}{\sqrt{25 + (10 \cdot \sqrt{5})}}

16.458m = 5 \cdot 7m \cdot \frac{1 + \sqrt{5}}{\sqrt{25 + (10 \cdot \sqrt{5})}}

16.458 = 5 \cdot 7 \cdot \frac{1 + \sqrt{5}}{\sqrt{25 + (10 \cdot \sqrt{5})}}

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Width of Pentagon given Inradius Solution

Follow our step by step solution on how to calculate Width of Pentagon given Inradius?

FIRST Step Consider the formula

w = 5 \cdot r i \cdot \frac{1 + \sqrt{5}}{\sqrt{25 + (10 \cdot \sqrt{5})}}

Next Step Substitute values of Variables

∴

w = 5 \cdot 7m \cdot \frac{1 + \sqrt{5}}{\sqrt{25 + (10 \cdot \sqrt{5})}}

Next Step Prepare to Evaluate

∴

w = 5 \cdot 7 \cdot \frac{1 + \sqrt{5}}{\sqrt{25 + (10 \cdot \sqrt{5})}}

Next Step Evaluate

∴

w = 16.4579870641892m

LAST Step Rounding Answer

∴

w = 16.458m

Width of Pentagon given Inradius Formula Elements

Variables

Functions

Width of Pentagon

Width of Pentagon is the measurement or extent of horizontal distance from left to right of the Pentagon.

Symbol: w

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Width of Pentagon

Inradius of Pentagon

The Inradius of Pentagon is defined as the radius of the circle which is inscribed inside the Pentagon.

Symbol: r_i

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Inradius of Pentagon

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.

Syntax: sqrt(Number)

Other Formulas to find Width of Pentagon

Go Width of Pentagon given Area

w = \frac{1 + \sqrt{5}}{2} \cdot \sqrt{4 \cdot \frac{A}{\sqrt{25 + (10 \cdot \sqrt{5})}}}

Go Width of Pentagon

w = \frac{1 + \sqrt{5}}{2} \cdot l e

Go Width of Pentagon given Circumradius

w = \frac{1 + \sqrt{5}}{2} \cdot (r c \cdot \frac{10}{\sqrt{50 + (10 \cdot \sqrt{5})}})

Go Width of Pentagon given Perimeter

w = P \cdot \frac{1 + \sqrt{5}}{10}

How to Evaluate Width of Pentagon given Inradius?

Width of Pentagon given Inradius evaluator uses Width of Pentagon = 5*Inradius of Pentagon*(1+sqrt(5))/sqrt(25+(10*sqrt(5))) to evaluate 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 evaluate Width of Pentagon given Inradius using this online evaluator? To use this online evaluator for Width of Pentagon given Inradius, enter Inradius of Pentagon (r_i) and hit the calculate button.

FAQs on Width of Pentagon given Inradius

What is the formula to find Width of Pentagon given Inradius?

The formula of Width of Pentagon given Inradius is expressed as Width of Pentagon = 5*Inradius of Pentagon*(1+sqrt(5))/sqrt(25+(10*sqrt(5))). Here is an example- 16.45799 = 5*7*(1+sqrt(5))/sqrt(25+(10*sqrt(5))).

How to calculate Width of Pentagon given Inradius?

With Inradius of Pentagon (r_i) we can find Width of Pentagon given Inradius using the formula - Width of Pentagon = 5*Inradius of Pentagon*(1+sqrt(5))/sqrt(25+(10*sqrt(5))). This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Width of Pentagon?

Here are the different ways to Calculate Width of Pentagon-

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))))

Can the Width of Pentagon given Inradius be negative?

No, the Width of Pentagon given Inradius, measured in Length cannot be negative.

Which unit is used to measure Width of Pentagon given Inradius?

Width of Pentagon given Inradius is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Width of Pentagon given Inradius can be measured.

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