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Total Surface Area of Antiprism given Height Formula

GoTotal Surface Area of Antiprism Formula

GoTotal Surface Area of Antiprism given Volume Formula

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The Total Surface Area of Antiprism is defined as the measure of the total 2d space occupied by all the faces of the Antiprism. Check FAQs

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

TSA - Total Surface Area of Antiprism?N_Vertices - Number of Vertices of Antiprism?h - Height of Antiprism?π - Archimedes' constant?

Total Surface Area of Antiprism given Height Example

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Here is how the Total Surface Area of Antiprism given Height equation looks like with Values.

Here is how the Total Surface Area of Antiprism given Height equation looks like with Units.

Here is how the Total Surface Area of Antiprism given Height equation looks like.

687.3197 = \frac{5}{2} \cdot (\cot (\frac{3.1416}{5}) + \sqrt{3}) \cdot {(\frac{8}{\sqrt{1 - \frac{{(\sec (\frac{3.1416}{2 \cdot 5}))}^{2}}{4}}})}^{2}

687.3197m² = \frac{5}{2} \cdot (\cot (\frac{3.1416}{5}) + \sqrt{3}) \cdot {(\frac{8m}{\sqrt{1 - \frac{{(\sec (\frac{3.1416}{2 \cdot 5}))}^{2}}{4}}})}^{2}

687.3197 = \frac{5}{2} \cdot (\cot (\frac{3.1416}{5}) + \sqrt{3}) \cdot {(\frac{8}{\sqrt{1 - \frac{{(\sec (\frac{3.1416}{2 \cdot 5}))}^{2}}{4}}})}^{2}

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Total Surface Area of Antiprism given Height Solution

Follow our step by step solution on how to calculate Total Surface Area of Antiprism given Height?

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

TSA = \frac{5}{2} \cdot (\cot (\frac{π}{5}) + \sqrt{3}) \cdot {(\frac{8m}{\sqrt{1 - \frac{{(\sec (\frac{π}{2 \cdot 5}))}^{2}}{4}}})}^{2}

Next Step Substitute values of Constants

∴

TSA = \frac{5}{2} \cdot (\cot (\frac{3.1416}{5}) + \sqrt{3}) \cdot {(\frac{8m}{\sqrt{1 - \frac{{(\sec (\frac{3.1416}{2 \cdot 5}))}^{2}}{4}}})}^{2}

Next Step Prepare to Evaluate

∴

TSA = \frac{5}{2} \cdot (\cot (\frac{3.1416}{5}) + \sqrt{3}) \cdot {(\frac{8}{\sqrt{1 - \frac{{(\sec (\frac{3.1416}{2 \cdot 5}))}^{2}}{4}}})}^{2}

Next Step Evaluate

∴

TSA = 687.319740545407m²

LAST Step Rounding Answer

∴

TSA = 687.3197m²

Total Surface Area of Antiprism given Height Formula Elements

Variables

Constants

Functions

Total Surface Area of Antiprism

The Total Surface Area of Antiprism is defined as the measure of the total 2d space occupied by all the faces of the Antiprism.

Symbol: TSA

Measurement: AreaUnit: m²

Note: Value should be greater than 0.

Formulas to find Total Surface Area 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

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

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

cot

Cotangent is a trigonometric function that is defined as the ratio of the adjacent side to the opposite side in a right triangle.

Syntax: cot(Angle)

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 Total Surface Area of Antiprism

Go Total Surface Area of Antiprism

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

Go Total Surface Area of Antiprism given Volume

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

Go Total Surface Area of Antiprism given Surface to Volume Ratio

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

How to Evaluate Total Surface Area of Antiprism given Height?

Total Surface Area of Antiprism given Height evaluator uses 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)))^2 to evaluate the Total Surface Area of Antiprism, The Total Surface Area of Antiprism given Height formula is defined as the measure of the total 2d space occupied by all the faces of the Antiprism, calculated using the height of Antiprism. Total Surface Area of Antiprism is denoted by TSA symbol.

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

FAQs on Total Surface Area of Antiprism given Height

What is the formula to find Total Surface Area of Antiprism given Height?

The formula of Total Surface Area of Antiprism given Height is expressed as 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)))^2. Here is an example- 687.3197 = 5/2*(cot(pi/5)+sqrt(3))*(8/(sqrt(1-((sec(pi/(2*5)))^2)/4)))^2.

How to calculate Total Surface Area of Antiprism given Height?

With Number of Vertices of Antiprism (N_Vertices) & Height of Antiprism (h) we can find Total Surface Area of Antiprism given Height using the formula - 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)))^2. This formula also uses Archimedes' constant and , Cotangent (cot), Secant (sec), Square Root (sqrt) function(s).

What are the other ways to Calculate Total Surface Area of Antiprism?

Here are the different ways to Calculate Total Surface Area of Antiprism-

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

Can the Total Surface Area of Antiprism given Height be negative?

No, the Total Surface Area of Antiprism given Height, measured in Area cannot be negative.

Which unit is used to measure Total Surface Area of Antiprism given Height?

Total Surface Area of Antiprism given Height is usually measured using the Square Meter[m²] for Area. Square Kilometer[m²], Square Centimeter[m²], Square Millimeter[m²] are the few other units in which Total Surface Area of Antiprism given Height can be measured.

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Total Surface Area of Antiprism given Height Formula

​GoTotal Surface Area of Antiprism Formula

​GoTotal Surface Area of Antiprism given Volume Formula

Total Surface Area of Antiprism given Height Example

Total Surface Area of Antiprism given Height Solution

Total Surface Area of Antiprism given Height Formula Elements

Other Formulas to find Total Surface Area of Antiprism

How to Evaluate Total Surface Area of Antiprism given Height?

FAQs on Total Surface Area of Antiprism given Height

Variable Name

GoTotal Surface Area of Antiprism Formula

GoTotal Surface Area of Antiprism given Volume Formula