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Diagonal of Pentagon given Height Formula

GoDiagonal of Pentagon given Circumradius Formula

GoDiagonal of Pentagon Formula

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Diagonal of Pentagon is a straight line joining two non adjacent vertices of a Pentagon. Check FAQs

d = (1 + \sqrt{5}) \cdot \frac{h}{\sqrt{5 + (2 \cdot \sqrt{5})}}

d - Diagonal of Pentagon?h - Height of Pentagon?

Diagonal of Pentagon given Height Example

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Here is how the Diagonal of Pentagon given Height equation looks like with Values.

Here is how the Diagonal of Pentagon given Height equation looks like with Units.

Here is how the Diagonal of Pentagon given Height equation looks like.

15.7719 = (1 + \sqrt{5}) \cdot \frac{15}{\sqrt{5 + (2 \cdot \sqrt{5})}}

15.7719m = (1 + \sqrt{5}) \cdot \frac{15m}{\sqrt{5 + (2 \cdot \sqrt{5})}}

15.7719 = (1 + \sqrt{5}) \cdot \frac{15}{\sqrt{5 + (2 \cdot \sqrt{5})}}

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Diagonal of Pentagon given Height Solution

Follow our step by step solution on how to calculate Diagonal of Pentagon given Height?

FIRST Step Consider the formula

d = (1 + \sqrt{5}) \cdot \frac{h}{\sqrt{5 + (2 \cdot \sqrt{5})}}

Next Step Substitute values of Variables

∴

d = (1 + \sqrt{5}) \cdot \frac{15m}{\sqrt{5 + (2 \cdot \sqrt{5})}}

Next Step Prepare to Evaluate

∴

d = (1 + \sqrt{5}) \cdot \frac{15}{\sqrt{5 + (2 \cdot \sqrt{5})}}

Next Step Evaluate

∴

d = 15.771933363574m

LAST Step Rounding Answer

∴

d = 15.7719m

Diagonal of Pentagon given Height Formula Elements

Variables

Functions

Diagonal of Pentagon

Diagonal of Pentagon is a straight line joining two non adjacent vertices of a Pentagon.

Symbol: d

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Diagonal of Pentagon

Height of Pentagon

Height of Pentagon is the distance between one side of Pentagon and its opposite vertex.

Symbol: h

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Height 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 Diagonal of Pentagon

Go Diagonal of Pentagon given Circumradius

d = \frac{r c}{\sqrt{\frac{5 - \sqrt{5}}{10}}}

Go Diagonal of Pentagon

d = (1 + \sqrt{5}) \cdot \frac{l e}{2}

Go Diagonal of Pentagon given Area

d = (1 + \sqrt{5}) \cdot \sqrt{\frac{A}{\sqrt{25 + (10 \cdot \sqrt{5})}}}

Go Diagonal of Pentagon given Perimeter

d = (1 + \sqrt{5}) \cdot \frac{P}{10}

How to Evaluate Diagonal of Pentagon given Height?

Diagonal of Pentagon given Height evaluator uses Diagonal of Pentagon = (1+sqrt(5))*Height of Pentagon/sqrt(5+(2*sqrt(5))) to evaluate the Diagonal of Pentagon, The Diagonal of Pentagon given Height is defined as the length of the line segment joining two non adjacent vertices of Pentagon, calculated using height. Diagonal of Pentagon is denoted by d symbol.

How to evaluate Diagonal of Pentagon given Height using this online evaluator? To use this online evaluator for Diagonal of Pentagon given Height, enter Height of Pentagon (h) and hit the calculate button.

FAQs on Diagonal of Pentagon given Height

What is the formula to find Diagonal of Pentagon given Height?

The formula of Diagonal of Pentagon given Height is expressed as Diagonal of Pentagon = (1+sqrt(5))*Height of Pentagon/sqrt(5+(2*sqrt(5))). Here is an example- 15.77193 = (1+sqrt(5))*15/sqrt(5+(2*sqrt(5))).

How to calculate Diagonal of Pentagon given Height?

With Height of Pentagon (h) we can find Diagonal of Pentagon given Height using the formula - Diagonal of Pentagon = (1+sqrt(5))*Height of Pentagon/sqrt(5+(2*sqrt(5))). This formula also uses Square Root (sqrt) function(s).

What are the other ways to Calculate Diagonal of Pentagon?

Here are the different ways to Calculate Diagonal of Pentagon-

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))))

Can the Diagonal of Pentagon given Height be negative?

No, the Diagonal of Pentagon given Height, measured in Length cannot be negative.

Which unit is used to measure Diagonal of Pentagon given Height?

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

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