Total Surface Area of Cuboid given Space Diagonal, Length and Height Solution

STEP 0: Pre-Calculation Summary
Formula Used
Total Surface Area of Cuboid = 2*((Length of Cuboid*Height of Cuboid)+(Height of Cuboid*sqrt(Space Diagonal of Cuboid^2-Length of Cuboid^2-Height of Cuboid^2))+(Length of Cuboid*sqrt(Space Diagonal of Cuboid^2-Length of Cuboid^2-Height of Cuboid^2)))
TSA = 2*((l*h)+(h*sqrt(dSpace^2-l^2-h^2))+(l*sqrt(dSpace^2-l^2-h^2)))
This formula uses 1 Functions, 4 Variables
Functions Used
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 Cuboid - (Measured in Square Meter) - Total Surface Area of Cuboid is the quantity of plane enclosed by the entire surface of the Cuboid.
Length of Cuboid - (Measured in Meter) - The Length of Cuboid is the measure of any one of the pair of parallel edges of base which are longer than the remaining pair of parallel edges of the Cuboid.
Height of Cuboid - (Measured in Meter) - The Height of Cuboid is the vertical distance measured from base to the top of Cuboid.
Space Diagonal of Cuboid - (Measured in Meter) - The Space Diagonal of Cuboid is the length of the line connecting one vertex to the opposite vertex through the interior of the Cuboid.
STEP 1: Convert Input(s) to Base Unit
Length of Cuboid: 12 Meter --> 12 Meter No Conversion Required
Height of Cuboid: 8 Meter --> 8 Meter No Conversion Required
Space Diagonal of Cuboid: 16 Meter --> 16 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
TSA = 2*((l*h)+(h*sqrt(dSpace^2-l^2-h^2))+(l*sqrt(dSpace^2-l^2-h^2))) --> 2*((12*8)+(8*sqrt(16^2-12^2-8^2))+(12*sqrt(16^2-12^2-8^2)))
Evaluating ... ...
TSA = 469.12812921102
STEP 3: Convert Result to Output's Unit
469.12812921102 Square Meter --> No Conversion Required
FINAL ANSWER
469.12812921102 469.1281 Square Meter <-- Total Surface Area of Cuboid
(Calculation completed in 00.004 seconds)

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Indian Institute of Technology, Indian School of Mines, DHANBAD (IIT ISM), Dhanbad, Jharkhand
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13 Total Surface Area of Cuboid Calculators

Total Surface Area of Cuboid given Space Diagonal, Length and Height
​ Go Total Surface Area of Cuboid = 2*((Length of Cuboid*Height of Cuboid)+(Height of Cuboid*sqrt(Space Diagonal of Cuboid^2-Length of Cuboid^2-Height of Cuboid^2))+(Length of Cuboid*sqrt(Space Diagonal of Cuboid^2-Length of Cuboid^2-Height of Cuboid^2)))
Total Surface Area of Cuboid given Space Diagonal, Length and Width
​ Go Total Surface Area of Cuboid = 2*((Length of Cuboid*sqrt(Space Diagonal of Cuboid^2-Length of Cuboid^2-Width of Cuboid^2))+(sqrt(Space Diagonal of Cuboid^2-Length of Cuboid^2-Width of Cuboid^2)*Width of Cuboid)+(Length of Cuboid*Width of Cuboid))
Total Surface Area of Cuboid given Space Diagonal, Height and Width
​ Go Total Surface Area of Cuboid = 2*((sqrt(Space Diagonal of Cuboid^2-Width of Cuboid^2-Height of Cuboid^2)*Height of Cuboid)+(Height of Cuboid*Width of Cuboid)+(sqrt(Space Diagonal of Cuboid^2-Width of Cuboid^2-Height of Cuboid^2)*Width of Cuboid))
Total Surface Area of Cuboid given Lateral Surface Area, Length and Height
​ Go Total Surface Area of Cuboid = 2*((Length of Cuboid*Height of Cuboid)+(Height of Cuboid*(Lateral Surface Area of Cuboid/(2*Height of Cuboid)-Length of Cuboid))+(Length of Cuboid*(Lateral Surface Area of Cuboid/(2*Height of Cuboid)-Length of Cuboid)))
Total Surface Area of Cuboid given Lateral Surface Area, Height and Width
​ Go Total Surface Area of Cuboid = 2*(((Lateral Surface Area of Cuboid/(2*Height of Cuboid)-Width of Cuboid)*Height of Cuboid)+(Height of Cuboid*Width of Cuboid)+((Lateral Surface Area of Cuboid/(2*Height of Cuboid)-Width of Cuboid)*Width of Cuboid))
Total Surface Area of Cuboid given Perimeter, Height, and Length
​ Go Total Surface Area of Cuboid = 2*((Length of Cuboid*Height of Cuboid)+(Height of Cuboid*(Perimeter of Cuboid-(4*(Length of Cuboid+Height of Cuboid)))/4)+(Length of Cuboid*(Perimeter of Cuboid-(4*(Length of Cuboid+Height of Cuboid)))/4))
Total Surface Area of Cuboid given Perimeter, Height, and Width
​ Go Total Surface Area of Cuboid = 2*(((Perimeter of Cuboid-(4*(Width of Cuboid+Height of Cuboid)))/4*Height of Cuboid)+(Height of Cuboid*Width of Cuboid)+((Perimeter of Cuboid-(4*(Width of Cuboid+Height of Cuboid)))/4*Width of Cuboid))
Total Surface Area of Cuboid given Perimeter, Length, and Width
​ Go Total Surface Area of Cuboid = 2*((Length of Cuboid*(Perimeter of Cuboid-(4*(Length of Cuboid+Width of Cuboid)))/4)+((Perimeter of Cuboid-(4*(Length of Cuboid+Width of Cuboid)))/4*Width of Cuboid)+(Length of Cuboid*Width of Cuboid))
Total Surface Area of Cuboid
​ Go Total Surface Area of Cuboid = 2*((Length of Cuboid*Height of Cuboid)+(Height of Cuboid*Width of Cuboid)+(Length of Cuboid*Width of Cuboid))
Total Surface Area of Cuboid given Volume, Length and Height
​ Go Total Surface Area of Cuboid = 2*(Volume of Cuboid/Length of Cuboid+(Height of Cuboid*Length of Cuboid)+Volume of Cuboid/Height of Cuboid)
Total Surface Area of Cuboid given Volume, Width and Height
​ Go Total Surface Area of Cuboid = 2*(Volume of Cuboid/Width of Cuboid+(Height of Cuboid*Width of Cuboid)+Volume of Cuboid/Height of Cuboid)
Total Surface Area of Cuboid given Volume, Length and Width
​ Go Total Surface Area of Cuboid = 2*(Volume of Cuboid/Length of Cuboid+(Length of Cuboid*Width of Cuboid)+Volume of Cuboid/Width of Cuboid)
Total Surface Area of Cuboid given Lateral Surface Area, Length and Width
​ Go Total Surface Area of Cuboid = Lateral Surface Area of Cuboid+(2*Length of Cuboid*Width of Cuboid)

4 Total Surface Area of Cuboid Calculators

Total Surface Area of Cuboid given Space Diagonal, Length and Height
​ Go Total Surface Area of Cuboid = 2*((Length of Cuboid*Height of Cuboid)+(Height of Cuboid*sqrt(Space Diagonal of Cuboid^2-Length of Cuboid^2-Height of Cuboid^2))+(Length of Cuboid*sqrt(Space Diagonal of Cuboid^2-Length of Cuboid^2-Height of Cuboid^2)))
Total Surface Area of Cuboid given Lateral Surface Area, Height and Width
​ Go Total Surface Area of Cuboid = 2*(((Lateral Surface Area of Cuboid/(2*Height of Cuboid)-Width of Cuboid)*Height of Cuboid)+(Height of Cuboid*Width of Cuboid)+((Lateral Surface Area of Cuboid/(2*Height of Cuboid)-Width of Cuboid)*Width of Cuboid))
Total Surface Area of Cuboid
​ Go Total Surface Area of Cuboid = 2*((Length of Cuboid*Height of Cuboid)+(Height of Cuboid*Width of Cuboid)+(Length of Cuboid*Width of Cuboid))
Total Surface Area of Cuboid given Volume, Length and Width
​ Go Total Surface Area of Cuboid = 2*(Volume of Cuboid/Length of Cuboid+(Length of Cuboid*Width of Cuboid)+Volume of Cuboid/Width of Cuboid)

Total Surface Area of Cuboid given Space Diagonal, Length and Height Formula

Total Surface Area of Cuboid = 2*((Length of Cuboid*Height of Cuboid)+(Height of Cuboid*sqrt(Space Diagonal of Cuboid^2-Length of Cuboid^2-Height of Cuboid^2))+(Length of Cuboid*sqrt(Space Diagonal of Cuboid^2-Length of Cuboid^2-Height of Cuboid^2)))
TSA = 2*((l*h)+(h*sqrt(dSpace^2-l^2-h^2))+(l*sqrt(dSpace^2-l^2-h^2)))

What is a Cuboid?

In geometry, a Cuboid is a convex polyhedron bounded by six quadrilateral faces, whose polyhedral graph is the same as that of a cube. While mathematical literature refers to any such polyhedron as a cuboid, other sources use "cuboid" to refer to a shape of this type in which each of the faces is a rectangle (and so each pair of adjacent faces meets in a right angle); this more restrictive type of cuboid is also known as a rectangular cuboid, right cuboid, rectangular box, rectangular hexahedron, right rectangular prism, or rectangular parallelepiped.

How to Calculate Total Surface Area of Cuboid given Space Diagonal, Length and Height?

Total Surface Area of Cuboid given Space Diagonal, Length and Height calculator uses Total Surface Area of Cuboid = 2*((Length of Cuboid*Height of Cuboid)+(Height of Cuboid*sqrt(Space Diagonal of Cuboid^2-Length of Cuboid^2-Height of Cuboid^2))+(Length of Cuboid*sqrt(Space Diagonal of Cuboid^2-Length of Cuboid^2-Height of Cuboid^2))) to calculate the Total Surface Area of Cuboid, The Total Surface Area of Cuboid given Space Diagonal, Length and Height formula is defined as the quantity of plane enclosed by the entire surface of the Cuboid, and is calculated using the space diagonal, length, and height of the Cuboid. Total Surface Area of Cuboid is denoted by TSA symbol.

How to calculate Total Surface Area of Cuboid given Space Diagonal, Length and Height using this online calculator? To use this online calculator for Total Surface Area of Cuboid given Space Diagonal, Length and Height, enter Length of Cuboid (l), Height of Cuboid (h) & Space Diagonal of Cuboid (dSpace) and hit the calculate button. Here is how the Total Surface Area of Cuboid given Space Diagonal, Length and Height calculation can be explained with given input values -> 469.1281 = 2*((12*8)+(8*sqrt(16^2-12^2-8^2))+(12*sqrt(16^2-12^2-8^2))).

FAQ

What is Total Surface Area of Cuboid given Space Diagonal, Length and Height?
The Total Surface Area of Cuboid given Space Diagonal, Length and Height formula is defined as the quantity of plane enclosed by the entire surface of the Cuboid, and is calculated using the space diagonal, length, and height of the Cuboid and is represented as TSA = 2*((l*h)+(h*sqrt(dSpace^2-l^2-h^2))+(l*sqrt(dSpace^2-l^2-h^2))) or Total Surface Area of Cuboid = 2*((Length of Cuboid*Height of Cuboid)+(Height of Cuboid*sqrt(Space Diagonal of Cuboid^2-Length of Cuboid^2-Height of Cuboid^2))+(Length of Cuboid*sqrt(Space Diagonal of Cuboid^2-Length of Cuboid^2-Height of Cuboid^2))). The Length of Cuboid is the measure of any one of the pair of parallel edges of base which are longer than the remaining pair of parallel edges of the Cuboid, The Height of Cuboid is the vertical distance measured from base to the top of Cuboid & The Space Diagonal of Cuboid is the length of the line connecting one vertex to the opposite vertex through the interior of the Cuboid.
How to calculate Total Surface Area of Cuboid given Space Diagonal, Length and Height?
The Total Surface Area of Cuboid given Space Diagonal, Length and Height formula is defined as the quantity of plane enclosed by the entire surface of the Cuboid, and is calculated using the space diagonal, length, and height of the Cuboid is calculated using Total Surface Area of Cuboid = 2*((Length of Cuboid*Height of Cuboid)+(Height of Cuboid*sqrt(Space Diagonal of Cuboid^2-Length of Cuboid^2-Height of Cuboid^2))+(Length of Cuboid*sqrt(Space Diagonal of Cuboid^2-Length of Cuboid^2-Height of Cuboid^2))). To calculate Total Surface Area of Cuboid given Space Diagonal, Length and Height, you need Length of Cuboid (l), Height of Cuboid (h) & Space Diagonal of Cuboid (dSpace). With our tool, you need to enter the respective value for Length of Cuboid, Height of Cuboid & Space Diagonal of Cuboid 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 Cuboid?
In this formula, Total Surface Area of Cuboid uses Length of Cuboid, Height of Cuboid & Space Diagonal of Cuboid. We can use 15 other way(s) to calculate the same, which is/are as follows -
  • Total Surface Area of Cuboid = 2*((Length of Cuboid*Height of Cuboid)+(Height of Cuboid*Width of Cuboid)+(Length of Cuboid*Width of Cuboid))
  • Total Surface Area of Cuboid = 2*(Volume of Cuboid/Width of Cuboid+(Height of Cuboid*Width of Cuboid)+Volume of Cuboid/Height of Cuboid)
  • Total Surface Area of Cuboid = 2*(Volume of Cuboid/Length of Cuboid+(Height of Cuboid*Length of Cuboid)+Volume of Cuboid/Height of Cuboid)
  • Total Surface Area of Cuboid = 2*(Volume of Cuboid/Length of Cuboid+(Length of Cuboid*Width of Cuboid)+Volume of Cuboid/Width of Cuboid)
  • Total Surface Area of Cuboid = 2*((Length of Cuboid*sqrt(Space Diagonal of Cuboid^2-Length of Cuboid^2-Width of Cuboid^2))+(sqrt(Space Diagonal of Cuboid^2-Length of Cuboid^2-Width of Cuboid^2)*Width of Cuboid)+(Length of Cuboid*Width of Cuboid))
  • Total Surface Area of Cuboid = 2*((sqrt(Space Diagonal of Cuboid^2-Width of Cuboid^2-Height of Cuboid^2)*Height of Cuboid)+(Height of Cuboid*Width of Cuboid)+(sqrt(Space Diagonal of Cuboid^2-Width of Cuboid^2-Height of Cuboid^2)*Width of Cuboid))
  • Total Surface Area of Cuboid = 2*(((Lateral Surface Area of Cuboid/(2*Height of Cuboid)-Width of Cuboid)*Height of Cuboid)+(Height of Cuboid*Width of Cuboid)+((Lateral Surface Area of Cuboid/(2*Height of Cuboid)-Width of Cuboid)*Width of Cuboid))
  • Total Surface Area of Cuboid = 2*((Length of Cuboid*Height of Cuboid)+(Height of Cuboid*(Lateral Surface Area of Cuboid/(2*Height of Cuboid)-Length of Cuboid))+(Length of Cuboid*(Lateral Surface Area of Cuboid/(2*Height of Cuboid)-Length of Cuboid)))
  • Total Surface Area of Cuboid = Lateral Surface Area of Cuboid+(2*Length of Cuboid*Width of Cuboid)
  • Total Surface Area of Cuboid = 2*(((Perimeter of Cuboid-(4*(Width of Cuboid+Height of Cuboid)))/4*Height of Cuboid)+(Height of Cuboid*Width of Cuboid)+((Perimeter of Cuboid-(4*(Width of Cuboid+Height of Cuboid)))/4*Width of Cuboid))
  • Total Surface Area of Cuboid = 2*((Length of Cuboid*Height of Cuboid)+(Height of Cuboid*(Perimeter of Cuboid-(4*(Length of Cuboid+Height of Cuboid)))/4)+(Length of Cuboid*(Perimeter of Cuboid-(4*(Length of Cuboid+Height of Cuboid)))/4))
  • Total Surface Area of Cuboid = 2*((Length of Cuboid*(Perimeter of Cuboid-(4*(Length of Cuboid+Width of Cuboid)))/4)+((Perimeter of Cuboid-(4*(Length of Cuboid+Width of Cuboid)))/4*Width of Cuboid)+(Length of Cuboid*Width of Cuboid))
  • Total Surface Area of Cuboid = 2*((Length of Cuboid*Height of Cuboid)+(Height of Cuboid*Width of Cuboid)+(Length of Cuboid*Width of Cuboid))
  • Total Surface Area of Cuboid = 2*(((Lateral Surface Area of Cuboid/(2*Height of Cuboid)-Width of Cuboid)*Height of Cuboid)+(Height of Cuboid*Width of Cuboid)+((Lateral Surface Area of Cuboid/(2*Height of Cuboid)-Width of Cuboid)*Width of Cuboid))
  • Total Surface Area of Cuboid = 2*(Volume of Cuboid/Length of Cuboid+(Length of Cuboid*Width of Cuboid)+Volume of Cuboid/Width of Cuboid)
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