Write all formulas related to the parellelopiped
Answers
Answer:
Volume and Surface Area Formula
For a given parallelepiped, let S is the area of the bottom face and H is the height, then the volume formula is given by;
V = S × H
Since the base of parallelepiped is in the shape of a parallelogram, therefore we can use the formula for the area of the parallelogram to find the base area.
Area of Parallelogram = Length × Height
Lateral Surface Area (LSA): Product of perimeter of the base and the height of the 6 parallelograms faced prism.
LSA = Perimeter of the base × Height
Total Surface Area (TSA): Addition of Lateral surface area and twice the base area
TSA = LSA + 2 Base Area
Rectangular Parallelepiped
When all the six faces of parallelepiped are in a rectangular shape, then it is considered a rectangular parallelepiped. It is a three-dimensional box-shaped structure. The length of all the parallel edges here are equal. The base of the prism here is rectangular in shape. A common example you can see in real life is the shoe box, which has a rectangular shape.
Volume of Rectangular Parallelepiped = Surface Area × Height
Here, the surface area is equal to the area of rectangle = Length × Width
Therefore, the volume becomes;
V = Length × Width × Height
So, if we know these three dimensions of the rectangular box, we can find its volume. Suppose, length = a, width = b and height = c, we can write the formula of volume, surface area and length of the diagonal of the rectangular box as;
Volume = abc
Surface area = 2ab + 2 bc + 2 ac
Diagonals = √ a² + b² + c²
Step-by-step explanation:
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