Total Surface Area of Antiprism given Height Calculator

✖Number of Vertices of Antiprism is defined as the number of vertices required to form the given Antiprism.ⓘ Number of Vertices of Antiprism [N_Vertices]			+10% -10%
✖Height of Antiprism is defined as the measure of the vertical distance from one top to the bottom face of the Antiprism.ⓘ Height of Antiprism [h]			+10% -10%

✖The Total Surface Area of Antiprism is defined as the measure of the total 2d space occupied by all the faces of the Antiprism.ⓘ Total Surface Area of Antiprism given Height [TSA]

⎘ Copy

👎

Formula

✖

Total Surface Area of Antiprism given Height

Formula

`"TSA" = "N"_{"Vertices"}/2*(cot(pi/"N"_{"Vertices"})+sqrt(3))*("h"/(sqrt(1-((sec(pi/(2*"N"_{"Vertices"})))^2)/4)))^2`

Example

`"687.3197m²"="5"/2*(cot(pi/"5")+sqrt(3))*("8m"/(sqrt(1-((sec(pi/(2*"5")))^2)/4)))^2`

Calculator

LaTeX

Reset

👍

Download 3D Geometry Formula PDF

Total Surface Area of Antiprism given Height Solution

STEP 0: Pre-Calculation Summary

Formula Used

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
TSA = N_Vertices/2*(cot(pi/N_Vertices)+sqrt(3))*(h/(sqrt(1-((sec(pi/(2*N_Vertices)))^2)/4)))^2
This formula uses 1 Constants, 3 Functions, 3 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

cot - Cotangent is a trigonometric function that is defined as the ratio of the adjacent side to the opposite side in a right triangle., 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., 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., sqrt(Number)

Variables Used

Total Surface Area of Antiprism - (Measured in Square Meter) - The Total Surface Area of Antiprism is defined as the measure of the total 2d space occupied by all the faces of the Antiprism.
Number of Vertices of Antiprism - Number of Vertices of Antiprism is defined as the number of vertices required to form the given Antiprism.
Height of Antiprism - (Measured in Meter) - Height of Antiprism is defined as the measure of the vertical distance from one top to the bottom face of the Antiprism.

STEP 1: Convert Input(s) to Base Unit

Number of Vertices of Antiprism: 5 --> No Conversion Required
Height of Antiprism: 8 Meter --> 8 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

TSA = N_Vertices/2*(cot(pi/N_Vertices)+sqrt(3))*(h/(sqrt(1-((sec(pi/(2*N_Vertices)))^2)/4)))^2 --> 5/2*(cot(pi/5)+sqrt(3))*(8/(sqrt(1-((sec(pi/(2*5)))^2)/4)))^2

Evaluating ... ...

TSA = 687.319740545407

STEP 3: Convert Result to Output's Unit

687.319740545407 Square Meter --> No Conversion Required

FINAL ANSWER

687.319740545407 ≈ 687.3197 Square Meter <-- Total Surface Area of Antiprism

(Calculation completed in 00.004 seconds)

You are here -

Home » Math » Geometry » 3D Geometry » Antiprism » Surface Area of Antiprism » Total Surface Area of Antiprism » Total Surface Area of Antiprism given Height

Credits

Created by Mona Gladys

St Joseph's College (SJC), Bengaluru

Mona Gladys has created this Calculator and 2000+ more calculators!

Verified by Mridul Sharma

Indian Institute of Information Technology (IIIT), Bhopal

Mridul Sharma has verified this Calculator and 1700+ more calculators!

< 4 Total Surface Area of Antiprism Calculators

Total Surface Area of Antiprism given Surface to Volume Ratio

Go 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

Total Surface Area of Antiprism given Volume

Go 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 given Height

Go 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

Total Surface Area of Antiprism

Go 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 given Height Formula

What is an Antiprism?

In geometry, an n-gonal antiprism or n-sided antiprism is a polyhedron composed of two parallel copies of some particular n-sided polygon, connected by an alternating band of triangles. Antiprisms are a subclass of prismatoids and are a (degenerate) type of snub polyhedron. Antiprisms are similar to prisms except that the bases are twisted relatively to each other, and that the side faces are triangles, rather than quadrilaterals. In the case of a regular n-sided base, one usually considers the case where its copy is twisted by an angle of 180/n degrees. Extra regularity is obtained when the line connecting the base centers is perpendicular to the base planes, making it a right antiprism. As faces, it has the two n-gonal bases and, connecting those bases, 2n isosceles triangles.

How to Calculate Total Surface Area of Antiprism given Height?

Total Surface Area of Antiprism given Height calculator 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 calculate 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 calculate Total Surface Area of Antiprism given Height using this online calculator? To use this online calculator 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. Here is how the Total Surface Area of Antiprism given Height calculation can be explained with given input values -> 687.3197 = 5/2*(cot(pi/5)+sqrt(3))*(8/(sqrt(1-((sec(pi/(2*5)))^2)/4)))^2.

FAQ

What is Total Surface Area of Antiprism given Height?

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 and is represented as TSA = N_Vertices/2*(cot(pi/N_Vertices)+sqrt(3))*(h/(sqrt(1-((sec(pi/(2*N_Vertices)))^2)/4)))^2 or 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. Number of Vertices of Antiprism is defined as the number of vertices required to form the given Antiprism & Height of Antiprism is defined as the measure of the vertical distance from one top to the bottom face of the Antiprism.

How to calculate Total Surface Area of Antiprism given Height?

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 is calculated using 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 calculate Total Surface Area of Antiprism given Height, you need Number of Vertices of Antiprism (N_Vertices) & Height of Antiprism (h). With our tool, you need to enter the respective value for Number of Vertices of Antiprism & Height of Antiprism and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Total Surface Area of Antiprism?

In this formula, Total Surface Area of Antiprism uses Number of Vertices of Antiprism & Height of Antiprism. We can use 3 other way(s) to calculate the same, which is/are as follows -

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

Home

FREE PDFs

🔍 Search