Parallelepiped is a three-dimensional structure whose each face is a parallelogram. A parallelepiped has 6 parallelogram faces, 8 vertices, and 12 edges. The structure of a parallelepiped is similar to a three-dimensional hollow or solid box. It is used in real-life applications. Objects such as matchboxes, bricks, mobile phones, and many more things from which we are surrounded are examples of rectangular parallelepiped. A parallelepiped can be said a prism with a parallelogram base.
In this article, we are going to learn about parallelepipeds, their types (Rectangular parallelepiped), properties of parallelepiped, surface area of parallelepiped, its lateral surface area, its total surface area, volume parallelepiped, and some problems based on parallelepiped.
What is Parallelepiped?
Parallelepiped appears to be related to the term parallelogram. It is a parallelogram-like three-dimensional structure, which has parallel planes. Parallelepiped is derived from the Greek word “Parallelepipdon” which means any object having parallel faces. This structure has six parallel faces which are joined together to form a solid structure. Rectangular parallelepiped has all its planes in a rectangular shape. Simple, parallelepiped has parallel faces in a parallelogram shape.
Parallelepiped Definition
Parallelepiped is a solid three dimensional, six faced body of which each face is parallelogram. It has 6 parallelogram face, 8 vertices and 12 edges. In figure shown below h is height, a is length and b is breadth of parallelepiped. It has 12 face diagonals
Rectangular Parallelepiped
This is one of type of parallelepiped. When all six faces are in the shape of rectangle then it forms rectangular parallelepiped. It is similar to structure of cuboid. The rectangular shaped three dimensional box is similar to structure of a rectangular parallelepiped. The figure shown below is example of a rectangular parallelepiped. The length of all parallel edges are equal. Length, width and height are defined in given figure below:
The volume and surface area formula for Rectangular Parallelepiped is given below:
Volume of Rectangular Parallelepiped = length × width × height
Surface Area of Rectangular Parallelepiped = 2 × (length×breadth + breadth×height + height×length)
Learn More about Rectangular Prism.
Properties of Parallelepiped
The properties of Parallelepiped are mentioned below:
- It has six faces of shape parallelogram.
- Parallelepiped has 8 vertices and 12 edges.
- Parallelepiped is sometimes called as prism with parallelogram base.
- It has total of twelve face diagonals.
- It is a six faced structure.
- There is one more type of parallelepiped known as rectangular parallelepiped.
- Each face of parallelepiped is mirror image of opposite face.
Surface Area of Parallelepiped
Surface Area of parallelepiped can be calculated by finding the area of the surfaces of Parallelepiped. There are two types of surface area one is lateral and another is total. Lateral surface area only includes the surrounding area, excluding its upper and lower base area. Total surface area contain both the upper and lower base area sum with its lateral surface area.
Surface Area of Parallelepiped Formula
The Surface Area of Parllelepiped Formula is given for the following
- Lateral Surface Area of Parallelepiped Formula
- Total Surface Area of Parallelepiped Formula
The Lateral surface area of parallelepiped = perimeter of base of parallelepiped × height area of parallelepiped
The Total surface area of parallelepiped = lateral surface area of parallelepiped + 2 × base area of parallelepiped
Lateral Surface Area of Parallelepiped Formula
Lateral Surafce Area of Parallelepiped is area of four out of six surfaces. LSA of Parallelepiped is calculated excluding top and base. Lateral surface area is defined in square units. Lateral surface is given as:
LSA of Parallelepiped = Perimeter of base × Height = 2(Length + Breadth) × Height
Total Surface area of Parallelepiped Formula
Total surface area is equal to the sum of lateral surface area with the two base areas present in parallelepiped in above and below of it. Total surface area is also defined in square units( because of sum of square unit with square unit). Total surface area is given as:
TSA of Parallelepiped = Lateral surface area of parallelepiped + Base area + Base area
TSA of Parallelepiped = 2(Length + Breadth) × Height + 2(Base Area)
Volume of Parallelepiped
For a given parallelepiped, volume is calculated by multiplying the bottom surface area with the height. Volume is defined in cubic units . Let us suppose that in a given parallelepiped a is the length, b is breadth, h is height then volume is given by Volume of Parallelepiped = length × breadth × height
Volume of Parallelepiped Formula
The formula of volume of parallelepiped is
Volume of Parallelepiped = Base Area × height
Where, h = height of parallelepiped,
b = base area of parallelepiped = length × breadth
Also, Check
Solved Examples on Parallelepiped
Example 1: What is the volume of rectangular parallelepiped whose length is 6m, breadth is 5 m and height is 3 m?
Solution:
Volume of rectangular parallelepiped = length × breadth × height
length = 6m, breadth = 5 m, height = 3m
volume = 6 × 5 × 3
So, volume of parallelepiped = 90 m3
Example 2: If the length and breadth of base of a parallelepiped is 10 m and 17 m respectively, and height of parallelepiped is 5m then find the lateral surface area of parallelepiped?
Solution:
Given that,
length = 10m, breadth = 17m, height = 5m
Lateral surface area of parallelepiped = 2 × (length + breadth) × height
Lateral surface area = 2 × (10 + 17) × 5
LSA of Parallelepiped = 2 × 27 × 5
LSA of Parallelepiped = 270 m2 .
Example 3: If the base area of parallelepiped is 89 m2 and height of parallelepiped is 12 m then what is the volume of parallelepiped?
Solution:
Given that,
base area = 89 m2, height = 12 m
Volume of parallelepiped = base area × height
volume = 89 × 12
Volume of Parallelepiped = 1068 m3
Example 4: If the base area of a parallelepiped is 36 m2 and height of parallelepiped is 4 m , then what is the volume occupied by it?
Solution:
Volume of parallelepiped = base area × height
volume of parallelepiped = 36 × 4
volume of parallelepiped = 144 m3 .
Example 5: What is surface area of a rectangular parallelepiped whose length is 13 inch, breadth is 15 inch and height is 17 inch?
Solution:
Surface area of rectangular parallelepiped = 2 × l + 2 × b + 2 × h
Surface area of rectangular parallelepiped = 2 × 13 + 2 × 15 + 2 × 17
Surface area of rectangular parallelepiped = 26 + 30 + 34
Surface area of rectangular parallelepiped = 90 inch2
Practice Problems on Parallelepiped
Problem 1. what is the volume of parallelepiped if base area of parallelepiped is 45 m2 and height of parallelepiped is13 m ?
Problem 2. If the lateral surface area of parallelepiped is 78 m2 and base area is 18 m2, then what is total surface area of parallelepiped ?
Problem 3. What is volume of rectangular parallelepiped if length, breadth and height is 46 m, 34 m and 12 m respectively?
Problem 4. If the length and breadth of base is 46 m and 34 m respectively and height is 12 m, then find the volume of parallelepiped.
Problem 5. If the length, breadth and height of a rectangular parallelepiped is 3m, 4m and 5m respectively then find the length of diagonal of it
Parallelepiped – FAQs
1. What is Meaning of Parallelepiped?
A parallelepiped is basically a prism with six parallelogram faces.
2. What is Parallelpiped in Real Life?
In real life, parallelepiped includes boxes, bricks, books etc.
3. What is Volume of Parallelepiped Formula?
The volume of Parallelepiped Formula = base area × height (cubic units)
4. Is Cuboid a Parallelepiped?
Yes Cuboid is a Paralleleiped with Rectangular Faces.
5. What is the Area of Parallelepiped?
The area of Parallelepiped is the total surface area and lateral surface are of Parallelepiped. The formula of lateral surface area and total surface area is given as
The Lateral surface area of parallelepiped = perimeter of base of parallelepiped × height area of parallelepiped
The Total surface area of parallelepiped = lateral surface area of parallelepiped + 2 × base area of parallelepiped
6. Is Parallelepiped a Polyhedron?
Yes, Parallelepiped is a Polyhedron with 6 parallelogram like faces.
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