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Height of Pentagon given Width Formula

GoHeight of Pentagon given Circumradius and Inradius Formula

GoHeight of Pentagon given Circumradius using Central Angle Formula

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

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

h - Height of Pentagon?w - Width of Pentagon?

Height of Pentagon given Width Example

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

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

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

15.2169 = 16 \cdot \frac{\sqrt{5 + (2 \cdot \sqrt{5})}}{1 + \sqrt{5}}

15.2169m = 16m \cdot \frac{\sqrt{5 + (2 \cdot \sqrt{5})}}{1 + \sqrt{5}}

15.2169 = 16 \cdot \frac{\sqrt{5 + (2 \cdot \sqrt{5})}}{1 + \sqrt{5}}

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Height of Pentagon given Width Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

h = 16m \cdot \frac{\sqrt{5 + (2 \cdot \sqrt{5})}}{1 + \sqrt{5}}

Next Step Prepare to Evaluate

∴

h = 16 \cdot \frac{\sqrt{5 + (2 \cdot \sqrt{5})}}{1 + \sqrt{5}}

Next Step Evaluate

∴

h = 15.2169042607225m

LAST Step Rounding Answer

∴

h = 15.2169m

Height of Pentagon given Width Formula Elements

Variables

Functions

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

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

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 Height of Pentagon

Go Height of Pentagon given Circumradius and Inradius

h = r c + r i

Go Height of Pentagon given Circumradius using Central Angle

h = r c \cdot (1 + \cos (\frac{π}{5}))

Go Height of Pentagon given Inradius using Central angle

h = r i \cdot (1 + (\frac{1}{\cos (\frac{π}{5})}))

Go Height of Pentagon given Edge Length using Central Angle

h = \frac{l e}{2} \cdot \frac{1 + \cos (\frac{π}{5})}{\sin (\frac{π}{5})}

How to Evaluate Height of Pentagon given Width?

Height of Pentagon given Width evaluator uses Height of Pentagon = Width of Pentagon*sqrt(5+(2*sqrt(5)))/(1+sqrt(5)) to evaluate the Height of Pentagon, The Height of Pentagon given Width formula is defined as the perpendicular distance from one of the vertices to the opposite edge of the Pentagon, calculated using width. Height of Pentagon is denoted by h symbol.

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

FAQs on Height of Pentagon given Width

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

The formula of Height of Pentagon given Width is expressed as Height of Pentagon = Width of Pentagon*sqrt(5+(2*sqrt(5)))/(1+sqrt(5)). Here is an example- 15.2169 = 16*sqrt(5+(2*sqrt(5)))/(1+sqrt(5)).

How to calculate Height of Pentagon given Width?

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

What are the other ways to Calculate Height of Pentagon?

Here are the different ways to Calculate Height of Pentagon-

Height of Pentagon=Circumradius of Pentagon+Inradius of Pentagon
Height of Pentagon=Circumradius of Pentagon*(1+cos(pi/5))
Height of Pentagon=Inradius of Pentagon*(1+(1/cos(pi/5)))

Can the Height of Pentagon given Width be negative?

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

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

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

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