Total Surface Area of Parallelepiped given Perimeter, Side A and Side C Calculator

✖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%
✖Perimeter of Parallelepiped is the total distance around the edge of the Parallelepiped.ⓘ Perimeter of Parallelepiped [P]			+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 [S_c]			+10% -10%
✖Angle Gamma of Parallelepiped is the angle formed by side A and side B at any of the two sharp tips of the Parallelepiped.ⓘ Angle Gamma of Parallelepiped [∠γ]			+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%
✖Angle Alpha of Parallelepiped is the angle formed by side B and side C at any of the two sharp tips of the Parallelepiped.ⓘ Angle Alpha of Parallelepiped [∠α]			+10% -10%

✖Total Surface Area of Parallelepiped is the total quantity of plane enclosed by the entire surface of the Parallelepiped.ⓘ Total Surface Area of Parallelepiped given Perimeter, Side A and Side C [TSA]

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Total Surface Area of Parallelepiped given Perimeter, Side A and Side C

Formula

`"TSA" = 2*(("S"_{"a"}*("P"/4-"S"_{"a"}-"S"_{"c"})*sin("∠γ"))+("S"_{"a"}*"S"_{"c"}*sin("∠β"))+(("P"/4-"S"_{"a"}-"S"_{"c"})*"S"_{"c"}*sin("∠α")))`

Example

`"1961.569m²"=2*(("30m"*("240m"/4-"30m"-"10m")*sin("75°"))+("30m"*"10m"*sin("60°"))+(("240m"/4-"30m"-"10m")*"10m"*sin("45°")))`

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Total Surface Area of Parallelepiped given Perimeter, Side A and Side C Solution

STEP 0: Pre-Calculation Summary

Formula Used

Total Surface Area of Parallelepiped = 2*((Side A of Parallelepiped*(Perimeter of Parallelepiped/4-Side A of Parallelepiped-Side C of Parallelepiped)*sin(Angle Gamma of Parallelepiped))+(Side A of Parallelepiped*Side C of Parallelepiped*sin(Angle Beta of Parallelepiped))+((Perimeter of Parallelepiped/4-Side A of Parallelepiped-Side C of Parallelepiped)*Side C of Parallelepiped*sin(Angle Alpha of Parallelepiped)))
TSA = 2*((S_a*(P/4-S_a-S_c)*sin(∠γ))+(S_a*S_c*sin(∠β))+((P/4-S_a-S_c)*S_c*sin(∠α)))
This formula uses 1 Functions, 7 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

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.
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.
Perimeter of Parallelepiped - (Measured in Meter) - Perimeter of Parallelepiped is the total distance around the edge of the Parallelepiped.
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.
Angle Gamma of Parallelepiped - (Measured in Radian) - Angle Gamma of Parallelepiped is the angle formed by side A and side B at any of the two sharp tips 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.
Angle Alpha of Parallelepiped - (Measured in Radian) - Angle Alpha of Parallelepiped is the angle formed by side B and side C at any of the two sharp tips of the Parallelepiped.

STEP 1: Convert Input(s) to Base Unit

Side A of Parallelepiped: 30 Meter --> 30 Meter No Conversion Required
Perimeter of Parallelepiped: 240 Meter --> 240 Meter No Conversion Required
Side C of Parallelepiped: 10 Meter --> 10 Meter No Conversion Required
Angle Gamma of Parallelepiped: 75 Degree --> 1.3089969389955 Radian (Check conversion here)
Angle Beta of Parallelepiped: 60 Degree --> 1.0471975511964 Radian (Check conversion here)
Angle Alpha of Parallelepiped: 45 Degree --> 0.785398163397301 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

TSA = 2*((S_a*(P/4-S_a-S_c)*sin(∠γ))+(S_a*S_c*sin(∠β))+((P/4-S_a-S_c)*S_c*sin(∠α))) --> 2*((30*(240/4-30-10)*sin(1.3089969389955))+(30*10*sin(1.0471975511964))+((240/4-30-10)*10*sin(0.785398163397301)))

Evaluating ... ...

TSA = 1961.56894629199

STEP 3: Convert Result to Output's Unit

1961.56894629199 Square Meter --> No Conversion Required

FINAL ANSWER

1961.56894629199 ≈ 1961.569 Square Meter <-- Total Surface Area of Parallelepiped

(Calculation completed in 00.020 seconds)

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Home » Math » Geometry » 3D Geometry » Parallelepiped » Surface Area of Parallelepiped » Total Surface Area of Parallelepiped » Total Surface Area of Parallelepiped given Perimeter, Side A and Side C

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

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< 8 Total Surface Area of Parallelepiped Calculators

Total Surface Area of Parallelepiped given Volume, Side A and Side B

Go Total Surface Area of Parallelepiped = 2*((Side A of Parallelepiped*Side B of Parallelepiped*sin(Angle Gamma of Parallelepiped))+(Volume of Parallelepiped*sin(Angle Beta of Parallelepiped))/(Side B 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)))+(Volume of Parallelepiped*sin(Angle Alpha 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))))

Total Surface Area of Parallelepiped given Volume, Side B and Side C

Go Total Surface Area of Parallelepiped = 2*((Volume of Parallelepiped*sin(Angle Gamma 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)))+(Volume of Parallelepiped*sin(Angle Beta of Parallelepiped))/(Side B 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*Side C of Parallelepiped*sin(Angle Alpha of Parallelepiped)))

Total Surface Area of Parallelepiped given Volume, Side A and Side C

Go Total Surface Area of Parallelepiped = 2*((Volume of Parallelepiped*sin(Angle Gamma 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 A of Parallelepiped*Side C of Parallelepiped*sin(Angle Beta of Parallelepiped))+(Volume of Parallelepiped*sin(Angle Alpha 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))))

Total Surface Area of Parallelepiped given Perimeter, Side A and Side B

Go Total Surface Area of Parallelepiped = 2*((Side A of Parallelepiped*Side B of Parallelepiped*sin(Angle Gamma of Parallelepiped))+(Side A of Parallelepiped*(Perimeter of Parallelepiped/4-Side A of Parallelepiped-Side B of Parallelepiped)*sin(Angle Beta of Parallelepiped))+(Side B of Parallelepiped*(Perimeter of Parallelepiped/4-Side A of Parallelepiped-Side B of Parallelepiped)*sin(Angle Alpha of Parallelepiped)))

Total Surface Area of Parallelepiped given Perimeter, Side B and Side C

Go Total Surface Area of Parallelepiped = 2*(((Perimeter of Parallelepiped/4-Side B of Parallelepiped-Side C of Parallelepiped)*Side B of Parallelepiped*sin(Angle Gamma of Parallelepiped))+((Perimeter of Parallelepiped/4-Side B of Parallelepiped-Side C of Parallelepiped)*Side C of Parallelepiped*sin(Angle Beta of Parallelepiped))+(Side B of Parallelepiped*Side C of Parallelepiped*sin(Angle Alpha of Parallelepiped)))

Total Surface Area of Parallelepiped given Perimeter, Side A and Side C

Go Total Surface Area of Parallelepiped = 2*((Side A of Parallelepiped*(Perimeter of Parallelepiped/4-Side A of Parallelepiped-Side C of Parallelepiped)*sin(Angle Gamma of Parallelepiped))+(Side A of Parallelepiped*Side C of Parallelepiped*sin(Angle Beta of Parallelepiped))+((Perimeter of Parallelepiped/4-Side A of Parallelepiped-Side C of Parallelepiped)*Side C of Parallelepiped*sin(Angle Alpha of Parallelepiped)))

Total Surface Area of Parallelepiped

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

Total Surface Area of Parallelepiped given Lateral Surface Area

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

Total Surface Area of Parallelepiped given Perimeter, Side A and Side C 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 Total Surface Area of Parallelepiped given Perimeter, Side A and Side C?

Total Surface Area of Parallelepiped given Perimeter, Side A and Side C calculator uses Total Surface Area of Parallelepiped = 2*((Side A of Parallelepiped*(Perimeter of Parallelepiped/4-Side A of Parallelepiped-Side C of Parallelepiped)*sin(Angle Gamma of Parallelepiped))+(Side A of Parallelepiped*Side C of Parallelepiped*sin(Angle Beta of Parallelepiped))+((Perimeter of Parallelepiped/4-Side A of Parallelepiped-Side C of Parallelepiped)*Side C of Parallelepiped*sin(Angle Alpha of Parallelepiped))) to calculate the Total Surface Area of Parallelepiped, The Total Surface Area of Parallelepiped given Perimeter, Side A and Side C formula is defined as measure of the total quantity of plane enclosed by the entire surface of the Parallelepiped, calculated using perimeter, side A and side C of Parallelepiped. Total Surface Area of Parallelepiped is denoted by TSA symbol.

How to calculate Total Surface Area of Parallelepiped given Perimeter, Side A and Side C using this online calculator? To use this online calculator for Total Surface Area of Parallelepiped given Perimeter, Side A and Side C, enter Side A of Parallelepiped (S_a), Perimeter of Parallelepiped (P), Side C of Parallelepiped (S_c), Angle Gamma of Parallelepiped (∠γ), Angle Beta of Parallelepiped (∠β) & Angle Alpha of Parallelepiped (∠α) and hit the calculate button. Here is how the Total Surface Area of Parallelepiped given Perimeter, Side A and Side C calculation can be explained with given input values -> 1961.569 = 2*((30*(240/4-30-10)*sin(1.3089969389955))+(30*10*sin(1.0471975511964))+((240/4-30-10)*10*sin(0.785398163397301))).

FAQ

What is Total Surface Area of Parallelepiped given Perimeter, Side A and Side C?

The Total Surface Area of Parallelepiped given Perimeter, Side A and Side C formula is defined as measure of the total quantity of plane enclosed by the entire surface of the Parallelepiped, calculated using perimeter, side A and side C of Parallelepiped and is represented as TSA = 2*((S_a*(P/4-S_a-S_c)*sin(∠γ))+(S_a*S_c*sin(∠β))+((P/4-S_a-S_c)*S_c*sin(∠α))) or Total Surface Area of Parallelepiped = 2*((Side A of Parallelepiped*(Perimeter of Parallelepiped/4-Side A of Parallelepiped-Side C of Parallelepiped)*sin(Angle Gamma of Parallelepiped))+(Side A of Parallelepiped*Side C of Parallelepiped*sin(Angle Beta of Parallelepiped))+((Perimeter of Parallelepiped/4-Side A of Parallelepiped-Side C of Parallelepiped)*Side C of Parallelepiped*sin(Angle Alpha of Parallelepiped))). Side A of Parallelepiped is the length of any one out of the three sides from any fixed vertex of the Parallelepiped, Perimeter of Parallelepiped is the total distance around the edge of the Parallelepiped, Side C of Parallelepiped is the length of any one out of the three sides from any fixed vertex of the Parallelepiped, Angle Gamma of Parallelepiped is the angle formed by side A and side B at any of the two sharp tips 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 & Angle Alpha of Parallelepiped is the angle formed by side B and side C at any of the two sharp tips of the Parallelepiped.

How to calculate Total Surface Area of Parallelepiped given Perimeter, Side A and Side C?

The Total Surface Area of Parallelepiped given Perimeter, Side A and Side C formula is defined as measure of the total quantity of plane enclosed by the entire surface of the Parallelepiped, calculated using perimeter, side A and side C of Parallelepiped is calculated using Total Surface Area of Parallelepiped = 2*((Side A of Parallelepiped*(Perimeter of Parallelepiped/4-Side A of Parallelepiped-Side C of Parallelepiped)*sin(Angle Gamma of Parallelepiped))+(Side A of Parallelepiped*Side C of Parallelepiped*sin(Angle Beta of Parallelepiped))+((Perimeter of Parallelepiped/4-Side A of Parallelepiped-Side C of Parallelepiped)*Side C of Parallelepiped*sin(Angle Alpha of Parallelepiped))). To calculate Total Surface Area of Parallelepiped given Perimeter, Side A and Side C, you need Side A of Parallelepiped (S_a), Perimeter of Parallelepiped (P), Side C of Parallelepiped (S_c), Angle Gamma of Parallelepiped (∠γ), Angle Beta of Parallelepiped (∠β) & Angle Alpha of Parallelepiped (∠α). With our tool, you need to enter the respective value for Side A of Parallelepiped, Perimeter of Parallelepiped, Side C of Parallelepiped, Angle Gamma of Parallelepiped, Angle Beta of Parallelepiped & Angle Alpha 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 Total Surface Area of Parallelepiped?

In this formula, Total Surface Area of Parallelepiped uses Side A of Parallelepiped, Perimeter of Parallelepiped, Side C of Parallelepiped, Angle Gamma of Parallelepiped, Angle Beta of Parallelepiped & Angle Alpha of Parallelepiped. We can use 7 other way(s) to calculate the same, which is/are as follows -

Total Surface Area of Parallelepiped = 2*((Side A of Parallelepiped*Side B of Parallelepiped*sin(Angle Gamma of Parallelepiped))+(Side A of Parallelepiped*Side C of Parallelepiped*sin(Angle Beta of Parallelepiped))+(Side B of Parallelepiped*Side C of Parallelepiped*sin(Angle Alpha of Parallelepiped)))
Total Surface Area of Parallelepiped = Lateral Surface Area of Parallelepiped+2*Side A of Parallelepiped*Side C of Parallelepiped*sin(Angle Beta of Parallelepiped)
Total Surface Area of Parallelepiped = 2*((Side A of Parallelepiped*Side B of Parallelepiped*sin(Angle Gamma of Parallelepiped))+(Volume of Parallelepiped*sin(Angle Beta of Parallelepiped))/(Side B 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)))+(Volume of Parallelepiped*sin(Angle Alpha 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))))
Total Surface Area of Parallelepiped = 2*((Volume of Parallelepiped*sin(Angle Gamma 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)))+(Volume of Parallelepiped*sin(Angle Beta of Parallelepiped))/(Side B 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*Side C of Parallelepiped*sin(Angle Alpha of Parallelepiped)))
Total Surface Area of Parallelepiped = 2*((Side A of Parallelepiped*Side B of Parallelepiped*sin(Angle Gamma of Parallelepiped))+(Side A of Parallelepiped*(Perimeter of Parallelepiped/4-Side A of Parallelepiped-Side B of Parallelepiped)*sin(Angle Beta of Parallelepiped))+(Side B of Parallelepiped*(Perimeter of Parallelepiped/4-Side A of Parallelepiped-Side B of Parallelepiped)*sin(Angle Alpha of Parallelepiped)))
Total Surface Area of Parallelepiped = 2*(((Perimeter of Parallelepiped/4-Side B of Parallelepiped-Side C of Parallelepiped)*Side B of Parallelepiped*sin(Angle Gamma of Parallelepiped))+((Perimeter of Parallelepiped/4-Side B of Parallelepiped-Side C of Parallelepiped)*Side C of Parallelepiped*sin(Angle Beta of Parallelepiped))+(Side B of Parallelepiped*Side C of Parallelepiped*sin(Angle Alpha of Parallelepiped)))
Total Surface Area of Parallelepiped = 2*((Volume of Parallelepiped*sin(Angle Gamma 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 A of Parallelepiped*Side C of Parallelepiped*sin(Angle Beta of Parallelepiped))+(Volume of Parallelepiped*sin(Angle Alpha 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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