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Height of Pentagon Formula

GoHeight of Pentagon given Circumradius and Inradius Formula

GoHeight of Pentagon given Edge Length 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 = \frac{l e}{2} \cdot \sqrt{5 + (2 \cdot \sqrt{5})}

h - Height of Pentagon?l_e - Edge Length of Pentagon?

Height of Pentagon Example

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

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

Here is how the Height of Pentagon equation looks like.

15.3884 = \frac{10}{2} \cdot \sqrt{5 + (2 \cdot \sqrt{5})}

15.3884m = \frac{10m}{2} \cdot \sqrt{5 + (2 \cdot \sqrt{5})}

15.3884 = \frac{10}{2} \cdot \sqrt{5 + (2 \cdot \sqrt{5})}

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Height of Pentagon Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

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

Next Step Prepare to Evaluate

∴

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

Next Step Evaluate

∴

h = 15.3884176858763m

LAST Step Rounding Answer

∴

h = 15.3884m

Height of Pentagon 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

Edge Length of Pentagon

The Edge Length of Pentagon is the length of one of the five sides of the Pentagon.

Symbol: l_e

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Edge Length 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 Edge Length using Central Angle

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

Go Height of Pentagon given Edge Length using Interior Angle

h = l e \cdot \frac{(\frac{3}{2} - \cos (\frac{3}{5} \cdot π)) \cdot (\frac{1}{2} - \cos (\frac{3}{5} \cdot π))}{\sin (\frac{3}{5} \cdot π)}

How to Evaluate Height of Pentagon?

Height of Pentagon evaluator uses Height of Pentagon = Edge Length of Pentagon/2*sqrt(5+(2*sqrt(5))) to evaluate the Height of Pentagon, Height of Pentagon is defined as the perpendicular distance from one of the vertices to the opposite edge of the Pentagon. Height of Pentagon is denoted by h symbol.

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

FAQs on Height of Pentagon

What is the formula to find Height of Pentagon?

The formula of Height of Pentagon is expressed as Height of Pentagon = Edge Length of Pentagon/2*sqrt(5+(2*sqrt(5))). Here is an example- 15.38842 = 10/2*sqrt(5+(2*sqrt(5))).

How to calculate Height of Pentagon?

With Edge Length of Pentagon (l_e) we can find Height of Pentagon using the formula - Height of Pentagon = Edge Length of Pentagon/2*sqrt(5+(2*sqrt(5))). This formula also uses Square Root Function 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=Edge Length of Pentagon/2*(1+cos(pi/5))/sin(pi/5)
Height of Pentagon=Edge Length of Pentagon*((3/2-cos(3/5*pi))*(1/2-cos(3/5*pi)))/sin(3/5*pi)

Can the Height of Pentagon be negative?

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

Which unit is used to measure Height of Pentagon?

Height of Pentagon 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 can be measured.

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