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What is a Parallelepiped? 

A parallelepiped is a three-dimensional shape that has six faces, all of which are parallelograms. It is an important concept in geometry and can be used to help understand other shapes. In this blog post, we'll break down the definition of a parallelepiped and explore some of its properties. 

Definition of a Parallelepiped 

A parallelepiped is a three-dimensional shape that has six faces, all of which are parallelograms. The length, width, and height of the parallelepiped form three sides of each face. The angles between the sides are 90° angles. This means that the figure can be thought of as a stack or column made up of identical cubes or rectangular prisms placed side by side with their edges touching each other. The opposite faces do not need to be equal in size; however, they must be parallel to each other. 

Properties 

The most important property of a parallelepiped is that it has 6 faces and 8 vertices (corners). Each face makes up one side of the figure, and each vertex is where two or more sides meet. All 12 edges (the lines connecting the vertices) are equal in length. Additionally, all angles between any two edges meeting at any given vertex are 90° angles. 

Another property to consider is volume—the amount of space enclosed by the figure’s boundaries. To calculate the volume, you simply multiply its length by its width by its height (L x W x H). The surface area can also be calculated; this is done by adding up the area of all 6 faces together (A1 + A2 + A3 + A4 + A5 + A6). 

                   

Conclusion: 

Parallelepipeds are often used as examples when teaching students about 3-dimensional shapes and their properties in geometry class. Understanding how to calculate volume and surface area for a parallelepiped can help students gain an appreciation for how geometry applies to everyday life and will provide them with valuable problem solving skills for future endeavors. As such, it's important for students to get familiar with this concept so they can use it as part of their studies!

FAQ

What is the use of parallelepiped?

A parallelepiped is a useful tool in geometry and can be used to help understand other shapes. It also has practical applications in everyday life, such as calculating the volume or surface area of an object. Additionally, it's often used to teach students about 3-dimensional shapes and their properties in a classroom setting.

What is difference between parallelepiped and cube?

The main difference between a parallelepiped and a cube is that the opposite faces of a parallelepiped do not need to be equal in size. Additionally, the angles between any two edges meeting at any given vertex in a parallelepiped are 90° angles, whereas in a cube they are all equal. A cube also has 6 faces, 8 vertices, and 12 edges but all the edges are equal in length. Volume for both is calculated by multiplying its length by its width by its height (L x W x H).

What is difference between parallelepiped and cuboid?

The main difference between a parallelepiped and a cuboid is that the opposite faces of a parallelepiped do not need to be equal in size. Additionally, the angles between any two edges meeting at any given vertex in a parallelepiped are 90° angles, whereas in a cuboid they can vary. A cuboid also has 6 faces, 8 vertices, and 12 edges but not all the edges are equal in length. Volume for both is calculated by multiplying its length by its width by its height (L x W x H). However, the surface area of a cuboid can be calculated by adding up the area of all 6 faces together (A1 + A2 + A3 + A4 + A5 + A6).  

How do you draw parallelepiped?

To draw a parallelepiped, start by drawing two parallel lines. Then draw perpendicular lines connecting the ends of these lines to form four 90° angles. Finally, connect the remaining corners with straight lines to complete the figure. Be sure to label each side and note that all 12 edges (the lines connecting the vertices) must be equal in length.



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