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Height of Pentagon given Circumradius 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 = 5 \cdot (\frac{\sqrt{5 + (2 \cdot \sqrt{5})}}{\sqrt{50 + (10 \cdot \sqrt{5})}}) \cdot r c

h - Height of Pentagon?r_c - Circumradius of Pentagon?

Height of Pentagon given Circumradius Example

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

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

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

16.2812 = 5 \cdot (\frac{\sqrt{5 + (2 \cdot \sqrt{5})}}{\sqrt{50 + (10 \cdot \sqrt{5})}}) \cdot 9

16.2812m = 5 \cdot (\frac{\sqrt{5 + (2 \cdot \sqrt{5})}}{\sqrt{50 + (10 \cdot \sqrt{5})}}) \cdot 9m

16.2812 = 5 \cdot (\frac{\sqrt{5 + (2 \cdot \sqrt{5})}}{\sqrt{50 + (10 \cdot \sqrt{5})}}) \cdot 9

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Height of Pentagon given Circumradius Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

h = 5 \cdot (\frac{\sqrt{5 + (2 \cdot \sqrt{5})}}{\sqrt{50 + (10 \cdot \sqrt{5})}}) \cdot 9m

Next Step Prepare to Evaluate

∴

h = 5 \cdot (\frac{\sqrt{5 + (2 \cdot \sqrt{5})}}{\sqrt{50 + (10 \cdot \sqrt{5})}}) \cdot 9

Next Step Evaluate

∴

h = 16.2811529493745m

LAST Step Rounding Answer

∴

h = 16.2812m

Height of Pentagon given Circumradius 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

Circumradius of Pentagon

The Circumradius of Pentagon is the radius of a circumcircle touching each of the vertices of Pentagon.

Symbol: r_c

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Circumradius 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 Circumradius?

Height of Pentagon given Circumradius evaluator uses Height of Pentagon = 5*(sqrt(5+(2*sqrt(5)))/sqrt(50+(10*sqrt(5))))*Circumradius of Pentagon to evaluate the Height of Pentagon, Height of Pentagon given Circumradius is defined as the perpendicular distance from one of the vertices to the opposite edge of the Pentagon, calculated using circumradius. Height of Pentagon is denoted by h symbol.

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

FAQs on Height of Pentagon given Circumradius

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

The formula of Height of Pentagon given Circumradius is expressed as Height of Pentagon = 5*(sqrt(5+(2*sqrt(5)))/sqrt(50+(10*sqrt(5))))*Circumradius of Pentagon. Here is an example- 16.28115 = 5*(sqrt(5+(2*sqrt(5)))/sqrt(50+(10*sqrt(5))))*9.

How to calculate Height of Pentagon given Circumradius?

With Circumradius of Pentagon (r_c) we can find Height of Pentagon given Circumradius using the formula - Height of Pentagon = 5*(sqrt(5+(2*sqrt(5)))/sqrt(50+(10*sqrt(5))))*Circumradius of Pentagon. 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 Circumradius be negative?

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

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

Height of Pentagon given Circumradius 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 Circumradius can be measured.

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