Side C of Parallelepiped given Total Surface Area and Lateral Surface Area Calculator

✖Total Surface Area of Parallelepiped is the total quantity of plane enclosed by the entire surface of the Parallelepiped.ⓘ Total Surface Area of Parallelepiped [TSA]			+10% -10%
✖Lateral Surface Area of Parallelepiped is the quantity of plane enclosed by all the lateral surfaces (that is, top and bottom faces are excluded) of the Parallelepiped.ⓘ Lateral Surface Area of Parallelepiped [LSA]			+10% -10%
✖Side A of Parallelepiped is the length of any one out of the three sides from any fixed vertex of the Parallelepiped.ⓘ Side A of Parallelepiped [S_a]			+10% -10%
✖Angle Beta of Parallelepiped is the angle formed by side A and side C at any of the two sharp tips of the Parallelepiped.ⓘ Angle Beta of Parallelepiped [∠β]			+10% -10%

✖Side C of Parallelepiped is the length of any one out of the three sides from any fixed vertex of the Parallelepiped.ⓘ Side C of Parallelepiped given Total Surface Area and Lateral Surface Area [S_c]

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Formula

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Side C of Parallelepiped given Total Surface Area and Lateral Surface Area

Formula

`"S"_{"c"} = ("TSA"-"LSA")/(2*"S"_{"a"}*sin("∠β"))`

Example

`"10.0074m"=("1960m²"-"1440m²")/(2*"30m"*sin("60°"))`

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Side C of Parallelepiped given Total Surface Area and Lateral Surface Area Solution

STEP 0: Pre-Calculation Summary

Formula Used

Side C of Parallelepiped = (Total Surface Area of Parallelepiped-Lateral Surface Area of Parallelepiped)/(2*Side A of Parallelepiped*sin(Angle Beta of Parallelepiped))
S_c = (TSA-LSA)/(2*S_a*sin(∠β))
This formula uses 1 Functions, 5 Variables

Functions Used

sin - Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse., sin(Angle)

Variables Used

Side C of Parallelepiped - (Measured in Meter) - Side C of Parallelepiped is the length of any one out of the three sides from any fixed vertex of the Parallelepiped.
Total Surface Area of Parallelepiped - (Measured in Square Meter) - Total Surface Area of Parallelepiped is the total quantity of plane enclosed by the entire surface of the Parallelepiped.
Lateral Surface Area of Parallelepiped - (Measured in Square Meter) - Lateral Surface Area of Parallelepiped is the quantity of plane enclosed by all the lateral surfaces (that is, top and bottom faces are excluded) of the Parallelepiped.
Side A of Parallelepiped - (Measured in Meter) - Side A of Parallelepiped is the length of any one out of the three sides from any fixed vertex of the Parallelepiped.
Angle Beta of Parallelepiped - (Measured in Radian) - Angle Beta of Parallelepiped is the angle formed by side A and side C at any of the two sharp tips of the Parallelepiped.

STEP 1: Convert Input(s) to Base Unit

Total Surface Area of Parallelepiped: 1960 Square Meter --> 1960 Square Meter No Conversion Required
Lateral Surface Area of Parallelepiped: 1440 Square Meter --> 1440 Square Meter No Conversion Required
Side A of Parallelepiped: 30 Meter --> 30 Meter No Conversion Required
Angle Beta of Parallelepiped: 60 Degree --> 1.0471975511964 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

S_c = (TSA-LSA)/(2*S_a*sin(∠β)) --> (1960-1440)/(2*30*sin(1.0471975511964))

Evaluating ... ...

S_c = 10.0074046659547

STEP 3: Convert Result to Output's Unit

10.0074046659547 Meter --> No Conversion Required

FINAL ANSWER

10.0074046659547 ≈ 10.0074 Meter <-- Side C of Parallelepiped

(Calculation completed in 00.004 seconds)

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Home » Math » Geometry » 3D Geometry » Parallelepiped » Side of Parallelepiped » Side C of Parallelepiped given Total Surface Area and Lateral Surface Area

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Created by Divanshi Jain

Netaji Subhash University of Technology, Delhi (NSUT Delhi), Dwarka

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Indian Institute of Technology, Indian School of Mines, DHANBAD (IIT ISM), Dhanbad, Jharkhand

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< 9 Side of Parallelepiped Calculators

Side A of Parallelepiped

Go Side A of Parallelepiped = Volume of Parallelepiped/(Side B of Parallelepiped*Side C of Parallelepiped*sqrt(1+(2*cos(Angle Alpha of Parallelepiped)*cos(Angle Beta of Parallelepiped)*cos(Angle Gamma of Parallelepiped))-(cos(Angle Alpha of Parallelepiped)^2+cos(Angle Beta of Parallelepiped)^2+cos(Angle Gamma of Parallelepiped)^2)))

Side B of Parallelepiped

Go Side B of Parallelepiped = Volume of Parallelepiped/(Side A of Parallelepiped*Side C of Parallelepiped*sqrt(1+(2*cos(Angle Alpha of Parallelepiped)*cos(Angle Beta of Parallelepiped)*cos(Angle Gamma of Parallelepiped))-(cos(Angle Alpha of Parallelepiped)^2+cos(Angle Beta of Parallelepiped)^2+cos(Angle Gamma of Parallelepiped)^2)))

Side C of Parallelepiped

Go Side C of Parallelepiped = Volume of Parallelepiped/(Side B of Parallelepiped*Side A of Parallelepiped*sqrt(1+(2*cos(Angle Alpha of Parallelepiped)*cos(Angle Beta of Parallelepiped)*cos(Angle Gamma of Parallelepiped))-(cos(Angle Alpha of Parallelepiped)^2+cos(Angle Beta of Parallelepiped)^2+cos(Angle Gamma of Parallelepiped)^2)))

Side B of Parallelepiped given Lateral Surface Area

Go Side B of Parallelepiped = Lateral Surface Area of Parallelepiped/(2*(Side A of Parallelepiped*sin(Angle Gamma of Parallelepiped)+Side C of Parallelepiped*sin(Angle Alpha of Parallelepiped)))

Side A of Parallelepiped given Total Surface Area and Lateral Surface Area

Go Side A of Parallelepiped = (Total Surface Area of Parallelepiped-Lateral Surface Area of Parallelepiped)/(2*Side C of Parallelepiped*sin(Angle Beta of Parallelepiped))

Side C of Parallelepiped given Total Surface Area and Lateral Surface Area

Go Side C of Parallelepiped = (Total Surface Area of Parallelepiped-Lateral Surface Area of Parallelepiped)/(2*Side A of Parallelepiped*sin(Angle Beta of Parallelepiped))

Side A of Parallelepiped given Perimeter, Side B and Side C

Go Side A of Parallelepiped = Perimeter of Parallelepiped/4-Side B of Parallelepiped-Side C of Parallelepiped

Side B of Parallelepiped given Perimeter, Side A and Side C

Go Side B of Parallelepiped = Perimeter of Parallelepiped/4-Side A of Parallelepiped-Side C of Parallelepiped

Side C of Parallelepiped given Perimeter, Side A and Side B

Go Side C of Parallelepiped = Perimeter of Parallelepiped/4-Side A of Parallelepiped-Side B of Parallelepiped

< 6 Side of Parallelepiped Calculators

Side A of Parallelepiped

Side B of Parallelepiped

Side C of Parallelepiped

Side B of Parallelepiped given Lateral Surface Area

Go Side B of Parallelepiped = Lateral Surface Area of Parallelepiped/(2*(Side A of Parallelepiped*sin(Angle Gamma of Parallelepiped)+Side C of Parallelepiped*sin(Angle Alpha of Parallelepiped)))

Side A of Parallelepiped given Total Surface Area and Lateral Surface Area

Go Side A of Parallelepiped = (Total Surface Area of Parallelepiped-Lateral Surface Area of Parallelepiped)/(2*Side C of Parallelepiped*sin(Angle Beta of Parallelepiped))

Side C of Parallelepiped given Total Surface Area and Lateral Surface Area

Go Side C of Parallelepiped = (Total Surface Area of Parallelepiped-Lateral Surface Area of Parallelepiped)/(2*Side A of Parallelepiped*sin(Angle Beta of Parallelepiped))

Side C of Parallelepiped given Total Surface Area and Lateral Surface Area Formula

What is a Parallelepiped?

A Parallelepiped is a three-dimensional figure formed by six parallelograms (the term rhomboid is also sometimes used with this meaning). By analogy, it relates to a parallelogram just as a cube relates to a square. In Euclidean geometry, the four concepts—parallelepiped and cube in three dimensions, parallelogram and square in two dimensions—are defined, but in the context of a more general affine geometry, in which angles are not differentiated, only parallelograms and parallelepipeds exist.

How to Calculate Side C of Parallelepiped given Total Surface Area and Lateral Surface Area?

Side C of Parallelepiped given Total Surface Area and Lateral Surface Area calculator uses Side C of Parallelepiped = (Total Surface Area of Parallelepiped-Lateral Surface Area of Parallelepiped)/(2*Side A of Parallelepiped*sin(Angle Beta of Parallelepiped)) to calculate the Side C of Parallelepiped, The Side C of Parallelepiped given Total Surface Area and Lateral Surface Area formula is defined as the length of any one out of the three sides from any fixed vertex of the Parallelepiped, calculated using total surface area and lateral surface area of Parallelepiped. Side C of Parallelepiped is denoted by S_c symbol.

How to calculate Side C of Parallelepiped given Total Surface Area and Lateral Surface Area using this online calculator? To use this online calculator for Side C of Parallelepiped given Total Surface Area and Lateral Surface Area, enter Total Surface Area of Parallelepiped (TSA), Lateral Surface Area of Parallelepiped (LSA), Side A of Parallelepiped (S_a) & Angle Beta of Parallelepiped (∠β) and hit the calculate button. Here is how the Side C of Parallelepiped given Total Surface Area and Lateral Surface Area calculation can be explained with given input values -> 10.0074 = (1960-1440)/(2*30*sin(1.0471975511964)).

FAQ

What is Side C of Parallelepiped given Total Surface Area and Lateral Surface Area?

The Side C of Parallelepiped given Total Surface Area and Lateral Surface Area formula is defined as the length of any one out of the three sides from any fixed vertex of the Parallelepiped, calculated using total surface area and lateral surface area of Parallelepiped and is represented as S_c = (TSA-LSA)/(2*S_a*sin(∠β)) or Side C of Parallelepiped = (Total Surface Area of Parallelepiped-Lateral Surface Area of Parallelepiped)/(2*Side A of Parallelepiped*sin(Angle Beta of Parallelepiped)). Total Surface Area of Parallelepiped is the total quantity of plane enclosed by the entire surface of the Parallelepiped, Lateral Surface Area of Parallelepiped is the quantity of plane enclosed by all the lateral surfaces (that is, top and bottom faces are excluded) of the Parallelepiped, Side A of Parallelepiped is the length of any one out of the three sides from any fixed vertex of the Parallelepiped & Angle Beta of Parallelepiped is the angle formed by side A and side C at any of the two sharp tips of the Parallelepiped.

How to calculate Side C of Parallelepiped given Total Surface Area and Lateral Surface Area?

The Side C of Parallelepiped given Total Surface Area and Lateral Surface Area formula is defined as the length of any one out of the three sides from any fixed vertex of the Parallelepiped, calculated using total surface area and lateral surface area of Parallelepiped is calculated using Side C of Parallelepiped = (Total Surface Area of Parallelepiped-Lateral Surface Area of Parallelepiped)/(2*Side A of Parallelepiped*sin(Angle Beta of Parallelepiped)). To calculate Side C of Parallelepiped given Total Surface Area and Lateral Surface Area, you need Total Surface Area of Parallelepiped (TSA), Lateral Surface Area of Parallelepiped (LSA), Side A of Parallelepiped (S_a) & Angle Beta of Parallelepiped (∠β). With our tool, you need to enter the respective value for Total Surface Area of Parallelepiped, Lateral Surface Area of Parallelepiped, Side A of Parallelepiped & Angle Beta of Parallelepiped 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 Side C of Parallelepiped?

In this formula, Side C of Parallelepiped uses Total Surface Area of Parallelepiped, Lateral Surface Area of Parallelepiped, Side A of Parallelepiped & Angle Beta of Parallelepiped. We can use 3 other way(s) to calculate the same, which is/are as follows -

Side C of Parallelepiped = Volume of Parallelepiped/(Side B of Parallelepiped*Side A of Parallelepiped*sqrt(1+(2*cos(Angle Alpha of Parallelepiped)*cos(Angle Beta of Parallelepiped)*cos(Angle Gamma of Parallelepiped))-(cos(Angle Alpha of Parallelepiped)^2+cos(Angle Beta of Parallelepiped)^2+cos(Angle Gamma of Parallelepiped)^2)))
Side C of Parallelepiped = Perimeter of Parallelepiped/4-Side A of Parallelepiped-Side B of Parallelepiped
Side C of Parallelepiped = Volume of Parallelepiped/(Side B of Parallelepiped*Side A of Parallelepiped*sqrt(1+(2*cos(Angle Alpha of Parallelepiped)*cos(Angle Beta of Parallelepiped)*cos(Angle Gamma of Parallelepiped))-(cos(Angle Alpha of Parallelepiped)^2+cos(Angle Beta of Parallelepiped)^2+cos(Angle Gamma of Parallelepiped)^2)))

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