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Edge Length of Antiprism Formula

GoEdge Length of Antiprism given Total Surface Area Formula

GoEdge Length of Antiprism given Volume Formula

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

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

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

Edge Length of Antiprism Example

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

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

Here is how the Edge Length of Antiprism equation looks like.

9.4046 = \frac{8}{\sqrt{1 - \frac{{(\sec (\frac{3.1416}{2 \cdot 5}))}^{2}}{4}}}

9.4046m = \frac{8m}{\sqrt{1 - \frac{{(\sec (\frac{3.1416}{2 \cdot 5}))}^{2}}{4}}}

9.4046 = \frac{8}{\sqrt{1 - \frac{{(\sec (\frac{3.1416}{2 \cdot 5}))}^{2}}{4}}}

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Edge Length of Antiprism Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

l e = \frac{8m}{\sqrt{1 - \frac{{(\sec (\frac{π}{2 \cdot 5}))}^{2}}{4}}}

Next Step Substitute values of Constants

∴

l e = \frac{8m}{\sqrt{1 - \frac{{(\sec (\frac{3.1416}{2 \cdot 5}))}^{2}}{4}}}

Next Step Prepare to Evaluate

∴

l e = \frac{8}{\sqrt{1 - \frac{{(\sec (\frac{3.1416}{2 \cdot 5}))}^{2}}{4}}}

Next Step Evaluate

∴

l e = 9.40456403667957m

LAST Step Rounding Answer

∴

l e = 9.4046m

Edge Length of Antiprism Formula Elements

Variables

Constants

Functions

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

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

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 Edge Length of Antiprism

Go Edge Length of Antiprism given Total Surface Area

l e = \sqrt{\frac{TSA}{\frac{N Vertices}{2} \cdot (\cot (\frac{π}{N Vertices}) + \sqrt{3})}}

Go Edge Length of Antiprism given Volume

l e = {(\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 Edge Length of Antiprism given Surface to Volume Ratio

l e = \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 Edge Length of Antiprism?

Edge Length of Antiprism evaluator uses Edge Length of Antiprism = Height of Antiprism/(sqrt(1-((sec(pi/(2*Number of Vertices of Antiprism)))^2)/4)) to evaluate the Edge Length of Antiprism, The Edge Length of Antiprism formula is defined as the straight line joining two adjacent vertices of Antiprism. Edge Length of Antiprism is denoted by l_e symbol.

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

FAQs on Edge Length of Antiprism

What is the formula to find Edge Length of Antiprism?

The formula of Edge Length of Antiprism is expressed as Edge Length of Antiprism = Height of Antiprism/(sqrt(1-((sec(pi/(2*Number of Vertices of Antiprism)))^2)/4)). Here is an example- 9.404564 = 8/(sqrt(1-((sec(pi/(2*5)))^2)/4)).

How to calculate Edge Length of Antiprism?

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

What are the other ways to Calculate Edge Length of Antiprism?

Here are the different ways to Calculate Edge Length of Antiprism-

Edge Length of Antiprism=sqrt(Total Surface Area of Antiprism/(Number of Vertices of Antiprism/2*(cot(pi/Number of Vertices of Antiprism)+sqrt(3))))
Edge Length of Antiprism=((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)
Edge Length of Antiprism=(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 Edge Length of Antiprism be negative?

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

Which unit is used to measure Edge Length of Antiprism?

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

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Edge Length of Antiprism Formula

​GoEdge Length of Antiprism given Total Surface Area Formula

​GoEdge Length of Antiprism given Volume Formula

Edge Length of Antiprism Example

Edge Length of Antiprism Solution

Edge Length of Antiprism Formula Elements

Other Formulas to find Edge Length of Antiprism

How to Evaluate Edge Length of Antiprism?

FAQs on Edge Length of Antiprism

Variable Name

GoEdge Length of Antiprism given Total Surface Area Formula

GoEdge Length of Antiprism given Volume Formula