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Height of Pentagon given Diagonal 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 = d \cdot \frac{\sqrt{5 + (2 \cdot \sqrt{5})}}{1 + \sqrt{5}}

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

Height of Pentagon given Diagonal Example

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

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

Here is how the Height of Pentagon given Diagonal 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 Diagonal Solution

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

FIRST Step Consider the formula

h = d \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 Diagonal 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

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

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 Diagonal?

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

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

FAQs on Height of Pentagon given Diagonal

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

The formula of Height of Pentagon given Diagonal is expressed as Height of Pentagon = Diagonal 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 Diagonal?

With Diagonal of Pentagon (d) we can find Height of Pentagon given Diagonal using the formula - Height of Pentagon = Diagonal 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 Diagonal be negative?

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

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

Height of Pentagon given Diagonal 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 Diagonal can be measured.

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