Half Height of Regular Bipyramid given Total Surface Area Calculator

✖Total Surface Area of Regular Bipyramid is the total amount of two-dimensional space occupied by all the faces of the Regular Bipyramid.ⓘ Total Surface Area of Regular Bipyramid [TSA]			+10% -10%
✖Edge Length of Base of Regular Bipyramid is the length of the straight line connecting any two adjacent base vertices of the Regular Bipyramid.ⓘ Edge Length of Base of Regular Bipyramid [l_e(Base)]			+10% -10%
✖Number of Base Vertices of Regular Bipyramid are the number of base vertices of a Regular Bipyramid.ⓘ Number of Base Vertices of Regular Bipyramid [n]			+10% -10%

✖Half Height of Regular Bipyramid is the total length of the perpendicular from the apex to the base of any one of the pyramids in the Regular Bipyramid.ⓘ Half Height of Regular Bipyramid given Total Surface Area [h_Half]

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Formula

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Half Height of Regular Bipyramid given Total Surface Area

Formula

`"h"_{"Half"} = sqrt(("TSA"/("l"_{"e(Base)"}*"n"))^2-(1/4*"l"_{"e(Base)"}^2*(cot(pi/"n"))^2))`

Example

`"7.180703m"=sqrt(("350m²"/("10m"*"4"))^2-(1/4*("10m")^2*(cot(pi/"4"))^2))`

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Half Height of Regular Bipyramid given Total Surface Area Solution

STEP 0: Pre-Calculation Summary

Formula Used

Half Height of Regular Bipyramid = sqrt((Total Surface Area of Regular Bipyramid/(Edge Length of Base of Regular Bipyramid*Number of Base Vertices of Regular Bipyramid))^2-(1/4*Edge Length of Base of Regular Bipyramid^2*(cot(pi/Number of Base Vertices of Regular Bipyramid))^2))
h_Half = sqrt((TSA/(l_e(Base)*n))^2-(1/4*l_e(Base)^2*(cot(pi/n))^2))
This formula uses 1 Constants, 2 Functions, 4 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)
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

Half Height of Regular Bipyramid - (Measured in Meter) - Half Height of Regular Bipyramid is the total length of the perpendicular from the apex to the base of any one of the pyramids in the Regular Bipyramid.
Total Surface Area of Regular Bipyramid - (Measured in Square Meter) - Total Surface Area of Regular Bipyramid is the total amount of two-dimensional space occupied by all the faces of the Regular Bipyramid.
Edge Length of Base of Regular Bipyramid - (Measured in Meter) - Edge Length of Base of Regular Bipyramid is the length of the straight line connecting any two adjacent base vertices of the Regular Bipyramid.
Number of Base Vertices of Regular Bipyramid - Number of Base Vertices of Regular Bipyramid are the number of base vertices of a Regular Bipyramid.

STEP 1: Convert Input(s) to Base Unit

Total Surface Area of Regular Bipyramid: 350 Square Meter --> 350 Square Meter No Conversion Required
Edge Length of Base of Regular Bipyramid: 10 Meter --> 10 Meter No Conversion Required
Number of Base Vertices of Regular Bipyramid: 4 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

h_Half = sqrt((TSA/(l_e(Base)*n))^2-(1/4*l_e(Base)^2*(cot(pi/n))^2)) --> sqrt((350/(10*4))^2-(1/4*10^2*(cot(pi/4))^2))

Evaluating ... ...

h_Half = 7.18070330817254

STEP 3: Convert Result to Output's Unit

7.18070330817254 Meter --> No Conversion Required

FINAL ANSWER

7.18070330817254 ≈ 7.180703 Meter <-- Half Height of Regular Bipyramid

(Calculation completed in 00.020 seconds)

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Home » Math » Geometry » 3D Geometry » Regular Bipyramid » Edge Length and Height of Regular Bipyramid » Half Height of Regular Bipyramid given Total Surface Area

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Created by Shweta Patil

Walchand College of Engineering (WCE), Sangli

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< 7 Edge Length and Height of Regular Bipyramid Calculators

Total Height of Regular Bipyramid given Total Surface Area

Go Total Height of Regular Bipyramid = 2*sqrt((Total Surface Area of Regular Bipyramid/(Edge Length of Base of Regular Bipyramid*Number of Base Vertices of Regular Bipyramid))^2-(1/4*Edge Length of Base of Regular Bipyramid^2*(cot(pi/Number of Base Vertices of Regular Bipyramid))^2))

Half Height of Regular Bipyramid given Total Surface Area

Go Half Height of Regular Bipyramid = sqrt((Total Surface Area of Regular Bipyramid/(Edge Length of Base of Regular Bipyramid*Number of Base Vertices of Regular Bipyramid))^2-(1/4*Edge Length of Base of Regular Bipyramid^2*(cot(pi/Number of Base Vertices of Regular Bipyramid))^2))

Edge Length of Base of Regular Bipyramid given Volume

Go Edge Length of Base of Regular Bipyramid = sqrt((4*Volume of Regular Bipyramid*tan(pi/Number of Base Vertices of Regular Bipyramid))/(2/3*Number of Base Vertices of Regular Bipyramid*Half Height of Regular Bipyramid))

Total Height of Regular Bipyramid given Volume

Go Total Height of Regular Bipyramid = (4*Volume of Regular Bipyramid*tan(pi/Number of Base Vertices of Regular Bipyramid))/(1/3*Number of Base Vertices of Regular Bipyramid*Edge Length of Base of Regular Bipyramid^2)

Half Height of Regular Bipyramid given Volume

Go Half Height of Regular Bipyramid = (4*Volume of Regular Bipyramid*tan(pi/Number of Base Vertices of Regular Bipyramid))/(2/3*Number of Base Vertices of Regular Bipyramid*Edge Length of Base of Regular Bipyramid^2)

Total Height of Regular Bipyramid

Go Total Height of Regular Bipyramid = 2*Half Height of Regular Bipyramid

Half Height of Regular Bipyramid

Go Half Height of Regular Bipyramid = Total Height of Regular Bipyramid/2

Half Height of Regular Bipyramid given Total Surface Area Formula

What is a Regular Bipyramid?

A Regular Bipyramid is a regular pyramid with its mirror image attached at its base. It is made of two N-gon-based pyramids that are stuck together at their bases. It consists of 2N faces which are all isosceles triangles. Also, It has 3N edges and N+2 vertices.

How to Calculate Half Height of Regular Bipyramid given Total Surface Area?

Half Height of Regular Bipyramid given Total Surface Area calculator uses Half Height of Regular Bipyramid = sqrt((Total Surface Area of Regular Bipyramid/(Edge Length of Base of Regular Bipyramid*Number of Base Vertices of Regular Bipyramid))^2-(1/4*Edge Length of Base of Regular Bipyramid^2*(cot(pi/Number of Base Vertices of Regular Bipyramid))^2)) to calculate the Half Height of Regular Bipyramid, Half Height of Regular Bipyramid given Total Surface Area formula is defined as the total length of the perpendicular from the apex to the base of any one of the pyramids in the Regular Bipyramid and is calculated using the total surface area of the Regular Bipyramid. Half Height of Regular Bipyramid is denoted by h_Half symbol.

How to calculate Half Height of Regular Bipyramid given Total Surface Area using this online calculator? To use this online calculator for Half Height of Regular Bipyramid given Total Surface Area, enter Total Surface Area of Regular Bipyramid (TSA), Edge Length of Base of Regular Bipyramid (l_e(Base)) & Number of Base Vertices of Regular Bipyramid (n) and hit the calculate button. Here is how the Half Height of Regular Bipyramid given Total Surface Area calculation can be explained with given input values -> 7.180703 = sqrt((350/(10*4))^2-(1/4*10^2*(cot(pi/4))^2)).

FAQ

What is Half Height of Regular Bipyramid given Total Surface Area?

Half Height of Regular Bipyramid given Total Surface Area formula is defined as the total length of the perpendicular from the apex to the base of any one of the pyramids in the Regular Bipyramid and is calculated using the total surface area of the Regular Bipyramid and is represented as h_Half = sqrt((TSA/(l_e(Base)*n))^2-(1/4*l_e(Base)^2*(cot(pi/n))^2)) or Half Height of Regular Bipyramid = sqrt((Total Surface Area of Regular Bipyramid/(Edge Length of Base of Regular Bipyramid*Number of Base Vertices of Regular Bipyramid))^2-(1/4*Edge Length of Base of Regular Bipyramid^2*(cot(pi/Number of Base Vertices of Regular Bipyramid))^2)). Total Surface Area of Regular Bipyramid is the total amount of two-dimensional space occupied by all the faces of the Regular Bipyramid, Edge Length of Base of Regular Bipyramid is the length of the straight line connecting any two adjacent base vertices of the Regular Bipyramid & Number of Base Vertices of Regular Bipyramid are the number of base vertices of a Regular Bipyramid.

How to calculate Half Height of Regular Bipyramid given Total Surface Area?

Half Height of Regular Bipyramid given Total Surface Area formula is defined as the total length of the perpendicular from the apex to the base of any one of the pyramids in the Regular Bipyramid and is calculated using the total surface area of the Regular Bipyramid is calculated using Half Height of Regular Bipyramid = sqrt((Total Surface Area of Regular Bipyramid/(Edge Length of Base of Regular Bipyramid*Number of Base Vertices of Regular Bipyramid))^2-(1/4*Edge Length of Base of Regular Bipyramid^2*(cot(pi/Number of Base Vertices of Regular Bipyramid))^2)). To calculate Half Height of Regular Bipyramid given Total Surface Area, you need Total Surface Area of Regular Bipyramid (TSA), Edge Length of Base of Regular Bipyramid (l_e(Base)) & Number of Base Vertices of Regular Bipyramid (n). With our tool, you need to enter the respective value for Total Surface Area of Regular Bipyramid, Edge Length of Base of Regular Bipyramid & Number of Base Vertices of Regular Bipyramid 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 Half Height of Regular Bipyramid?

In this formula, Half Height of Regular Bipyramid uses Total Surface Area of Regular Bipyramid, Edge Length of Base of Regular Bipyramid & Number of Base Vertices of Regular Bipyramid. We can use 2 other way(s) to calculate the same, which is/are as follows -

Half Height of Regular Bipyramid = Total Height of Regular Bipyramid/2
Half Height of Regular Bipyramid = (4*Volume of Regular Bipyramid*tan(pi/Number of Base Vertices of Regular Bipyramid))/(2/3*Number of Base Vertices of Regular Bipyramid*Edge Length of Base of Regular Bipyramid^2)

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