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## Height of Antiprism Solution

STEP 0: Pre-Calculation Summary
Formula Used
height = sqrt(1-((sec(pi/(2*Number Of Vertices)))^2)/4)*Side
h = sqrt(1-((sec(pi/(2*n)))^2)/4)*s
This formula uses 2 Constants, 2 Functions, 2 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
e - Napier's constant Value Taken As 2.71828182845904523536028747135266249
Functions Used
sec - Trigonometric secant function, sec(Angle)
sqrt - Squre root function, sqrt(Number)
Variables Used
Number Of Vertices- Number Of Vertices is the number of vertices in the given two dimensional figure.
Side - The side is an upright or sloping surface of a structure or object that is not the top or bottom and generally not the front or back. (Measured in Meter)
STEP 1: Convert Input(s) to Base Unit
Number Of Vertices: 1 --> No Conversion Required
Side: 9 Meter --> 9 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
h = sqrt(1-((sec(pi/(2*n)))^2)/4)*s --> sqrt(1-((sec(pi/(2*1)))^2)/4)*9
Evaluating ... ...
h = NaN
STEP 3: Convert Result to Output's Unit
NaN Meter --> No Conversion Required
NaN Meter <-- Height
(Calculation completed in 00.031 seconds)

## < 11 Other formulas that you can solve using the same Inputs

Total Surface Area of a Pyramid
total_surface_area = Side*(Side+sqrt(Side^2+4*(Height)^2)) Go
Area of a Rhombus when side and diagonals are given
area = (1/2)*(Diagonal A)*(sqrt(4*Side^2-(Diagonal A)^2)) Go
Lateral Surface Area of a Pyramid
lateral_surface_area = Side*sqrt(Side^2+4*(Height)^2) Go
Surface Area of a Capsule
Volume of a Capsule
Area of a Octagon
area = 2*(1+sqrt(2))*(Side)^2 Go
Volume of a Pyramid
volume = (1/3)*Side^2*Height Go
Area of a Hexagon
area = (3/2)*sqrt(3)*Side^2 Go
Base Surface Area of a Pyramid
base_surface_area = Side^2 Go
Surface Area of a Cube
surface_area = 6*Side^2 Go
Volume of a Cube
volume = Side^3 Go

## < 11 Other formulas that calculate the same Output

Height of a triangular prism when lateral surface area is given
height = Lateral Surface Area/(Side A+Side B+Side C) Go
Height of an isosceles trapezoid
height = sqrt(Side C^2-0.25*(Side A-Side B)^2) Go
Altitude of an isosceles triangle
height = sqrt((Side A)^2+((Side B)^2/4)) Go
Height of a triangular prism when base and volume are given
height = (2*Volume)/(Base*Length) Go
Height of a trapezoid when area and sum of parallel sides are given
height = (2*Area)/Sum of parallel sides of a trapezoid Go
Altitude of the largest right pyramid with a square base that can be inscribed in a sphere of radius a
height = 4*Radius of Sphere/3 Go
Height of Cone inscribed in a sphere for maximum volume of cone in terms of radius of sphere
height = 4*Radius of Sphere/3 Go
Height of Cone circumscribing a sphere such that volume of cone is minimum
height = 4*Radius of Sphere Go
Height of parabolic section that can be cut from a cone for maximum area of parabolic section
height = 0.75*Slant Height Go
Height of a circular cylinder of maximum convex surface area in a given circular cone
height = Height of Cone/2 Go
Height of Largest right circular cylinder that can be inscribed within a cone
height = Height of Cone/3 Go

### Height of Antiprism Formula

height = sqrt(1-((sec(pi/(2*Number Of Vertices)))^2)/4)*Side
h = sqrt(1-((sec(pi/(2*n)))^2)/4)*s

## 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 Height of Antiprism?

Height of Antiprism calculator uses height = sqrt(1-((sec(pi/(2*Number Of Vertices)))^2)/4)*Side to calculate the Height, The Height of Antiprism formula is defined as the measure of vertical distance from one top to bottom face of Antiprism, where h = height of Antiprism. Height and is denoted by h symbol.

How to calculate Height of Antiprism using this online calculator? To use this online calculator for Height of Antiprism, enter Number Of Vertices (n) and Side (s) and hit the calculate button. Here is how the Height of Antiprism calculation can be explained with given input values -> NaN = sqrt(1-((sec(pi/(2*1)))^2)/4)*9.

### FAQ

What is Height of Antiprism?
The Height of Antiprism formula is defined as the measure of vertical distance from one top to bottom face of Antiprism, where h = height of Antiprism and is represented as h = sqrt(1-((sec(pi/(2*n)))^2)/4)*s or height = sqrt(1-((sec(pi/(2*Number Of Vertices)))^2)/4)*Side. Number Of Vertices is the number of vertices in the given two dimensional figure and The side is an upright or sloping surface of a structure or object that is not the top or bottom and generally not the front or back.
How to calculate Height of Antiprism?
The Height of Antiprism formula is defined as the measure of vertical distance from one top to bottom face of Antiprism, where h = height of Antiprism is calculated using height = sqrt(1-((sec(pi/(2*Number Of Vertices)))^2)/4)*Side. To calculate Height of Antiprism, you need Number Of Vertices (n) and Side (s). With our tool, you need to enter the respective value for Number Of Vertices and Side 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 Height?
In this formula, Height uses Number Of Vertices and Side. We can use 11 other way(s) to calculate the same, which is/are as follows -
• height = 4*Radius of Sphere/3
• height = 4*Radius of Sphere
• height = Height of Cone/3
• height = 4*Radius of Sphere/3
• height = Height of Cone/2
• height = 0.75*Slant Height
• height = sqrt(Side C^2-0.25*(Side A-Side B)^2)
• height = (2*Area)/Sum of parallel sides of a trapezoid
• height = sqrt((Side A)^2+((Side B)^2/4))
• height = (2*Volume)/(Base*Length)
• height = Lateral Surface Area/(Side A+Side B+Side C)
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