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Height of Antiprism Formula

GoHeight of Antiprism given Total Surface Area Formula

GoHeight of Antiprism given Volume Formula

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Height of Antiprism is defined as the measure of the vertical distance from one top to the bottom face of the Antiprism. Check FAQs

h = \sqrt{1 - \frac{{(\sec (\frac{π}{2 \cdot N Vertices}))}^{2}}{4}} \cdot l e

h - Height of Antiprism?N_Vertices - Number of Vertices of Antiprism?l_e - Edge Length of Antiprism?π - Archimedes' constant?

Height of Antiprism Example

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

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

Here is how the Height of Antiprism equation looks like.

8.5065 = \sqrt{1 - \frac{{(\sec (\frac{3.1416}{2 \cdot 5}))}^{2}}{4}} \cdot 10

8.5065m = \sqrt{1 - \frac{{(\sec (\frac{3.1416}{2 \cdot 5}))}^{2}}{4}} \cdot 10m

8.5065 = \sqrt{1 - \frac{{(\sec (\frac{3.1416}{2 \cdot 5}))}^{2}}{4}} \cdot 10

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Height of Antiprism Solution

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

FIRST Step Consider the formula

h = \sqrt{1 - \frac{{(\sec (\frac{π}{2 \cdot N Vertices}))}^{2}}{4}} \cdot l e

Next Step Substitute values of Variables

∴

h = \sqrt{1 - \frac{{(\sec (\frac{π}{2 \cdot 5}))}^{2}}{4}} \cdot 10m

Next Step Substitute values of Constants

∴

h = \sqrt{1 - \frac{{(\sec (\frac{3.1416}{2 \cdot 5}))}^{2}}{4}} \cdot 10m

Next Step Prepare to Evaluate

∴

h = \sqrt{1 - \frac{{(\sec (\frac{3.1416}{2 \cdot 5}))}^{2}}{4}} \cdot 10

Next Step Evaluate

∴

h = 8.5065080835204m

LAST Step Rounding Answer

∴

h = 8.5065m

Height of Antiprism Formula Elements

Variables

Constants

Functions

Height of Antiprism

Height of Antiprism is defined as the measure of the vertical distance from one top to the bottom face of the Antiprism.

Symbol: h

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Height of Antiprism

Number of Vertices of Antiprism

Number of Vertices of Antiprism is defined as the number of vertices required to form the given Antiprism.

Symbol: N_Vertices

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Number of Vertices of Antiprism

Edge Length of Antiprism

Edge Length of Antiprism is defined as the straight line joining the adjacent vertices of the Antiprism.

Symbol: l_e

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Edge Length of Antiprism

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

sec

Secant is a trigonometric function that is defined ratio of the hypotenuse to the shorter side adjacent to an acute angle (in a right-angled triangle); the reciprocal of a cosine.

Syntax: sec(Angle)

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 Antiprism

Go Height of Antiprism given Total Surface Area

h = \sqrt{1 - \frac{{(\sec (\frac{π}{2 \cdot N Vertices}))}^{2}}{4}} \cdot \sqrt{\frac{TSA}{\frac{N Vertices}{2} \cdot (\cot (\frac{π}{N Vertices}) + \sqrt{3})}}

Go Height of Antiprism given Volume

h = \sqrt{1 - \frac{{(\sec (\frac{π}{2 \cdot N Vertices}))}^{2}}{4}} \cdot {(\frac{12 \cdot {(\sin (\frac{π}{N Vertices}))}^{2} \cdot V}{N Vertices \cdot \sin (\frac{3 \cdot π}{2 \cdot N Vertices}) \cdot \sqrt{4 \cdot ({\cos (\frac{π}{2 \cdot N Vertices})}^{2}) - 1}})}^{\frac{1}{3}}

Go Height of Antiprism given Surface to Volume Ratio

h = \sqrt{1 - \frac{{(\sec (\frac{π}{2 \cdot N Vertices}))}^{2}}{4}} \cdot \frac{6 \cdot {(\sin (\frac{π}{N Vertices}))}^{2} \cdot (\cot (\frac{π}{N Vertices}) + \sqrt{3})}{\sin (\frac{3 \cdot π}{2 \cdot N Vertices}) \cdot \sqrt{4 \cdot ({\cos (\frac{π}{2 \cdot N Vertices})}^{2}) - 1} \cdot R A/V}

How to Evaluate Height of Antiprism?

Height of Antiprism evaluator uses Height of Antiprism = sqrt(1-((sec(pi/(2*Number of Vertices of Antiprism)))^2)/4)*Edge Length of Antiprism to evaluate the Height of Antiprism, The Height of Antiprism formula is defined as the measure of vertical distance from one top to bottom face of the Antiprism. Height of Antiprism is denoted by h symbol.

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

FAQs on Height of Antiprism

What is the formula to find Height of Antiprism?

The formula of Height of Antiprism is expressed as Height of Antiprism = sqrt(1-((sec(pi/(2*Number of Vertices of Antiprism)))^2)/4)*Edge Length of Antiprism. Here is an example- 8.506508 = sqrt(1-((sec(pi/(2*5)))^2)/4)*10.

How to calculate Height of Antiprism?

With Number of Vertices of Antiprism (N_Vertices) & Edge Length of Antiprism (l_e) we can find Height of Antiprism using the formula - Height of Antiprism = sqrt(1-((sec(pi/(2*Number of Vertices of Antiprism)))^2)/4)*Edge Length of Antiprism. This formula also uses Archimedes' constant and , Secant (sec), Square Root (sqrt) function(s).

What are the other ways to Calculate Height of Antiprism?

Here are the different ways to Calculate Height of Antiprism-

Height of Antiprism=sqrt(1-((sec(pi/(2*Number of Vertices of Antiprism)))^2)/4)*sqrt(Total Surface Area of Antiprism/(Number of Vertices of Antiprism/2*(cot(pi/Number of Vertices of Antiprism)+sqrt(3))))
Height of Antiprism=sqrt(1-((sec(pi/(2*Number of Vertices of Antiprism)))^2)/4)*((12*(sin(pi/Number of Vertices of Antiprism))^2*Volume of Antiprism)/(Number of Vertices of Antiprism*sin((3*pi)/(2*Number of Vertices of Antiprism))*sqrt(4*(cos(pi/(2*Number of Vertices of Antiprism))^2)-1)))^(1/3)
Height of Antiprism=sqrt(1-((sec(pi/(2*Number of Vertices of Antiprism)))^2)/4)*(6*(sin(pi/Number of Vertices of Antiprism))^2*(cot(pi/Number of Vertices of Antiprism)+sqrt(3)))/(sin((3*pi)/(2*Number of Vertices of Antiprism))*sqrt(4*(cos(pi/(2*Number of Vertices of Antiprism))^2)-1)*Surface to Volume Ratio of Antiprism)

Can the Height of Antiprism be negative?

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

Which unit is used to measure Height of Antiprism?

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

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Height of Antiprism Formula

​GoHeight of Antiprism given Total Surface Area Formula

​GoHeight of Antiprism given Volume Formula

Height of Antiprism Example

Height of Antiprism Solution

Height of Antiprism Formula Elements

Other Formulas to find Height of Antiprism

How to Evaluate Height of Antiprism?

FAQs on Height of Antiprism

Variable Name

GoHeight of Antiprism given Total Surface Area Formula

GoHeight of Antiprism given Volume Formula