Learn How Many Vertices Does A Rectangular Prism Have?


Before answering this question it is important to understand what type of shape a prism is. Prisms are polyhedrons: three dimensions solids that are formed by faces, edges and vertices. Each face of a polyhedron is a flat two-dimensional shape, or polygon. The edge is the joint of two sides, and finally the vertex are the points where two or more edges meet.

Simply explained, a prism is one of the most interesting polyhedrons with the following characteristics:

  1. It has equal and parallel ends, each of them is called base.
  2. Its sides, or faces, are formed by flat faces, never curved sides. These are parallelograms, in other words, shapes which opposite side are parallel and have the same length, and its opposite angles are identical.
  3. Its cross section is the same all along its height. This means that if we cut straight through it we will always be able to see the same shape.

Knowing the rectangular prism geometry

A rectangular prism is also known as cuboid. Its surface is formed by two equal and parallel rectangles as the bases, and four side faces which are also parallel and equal rectangles, making it a total of six faces.

The cuboid is a right prism and a particular case of an irregular quadrangular prism, as its cross section is not a shape with equal edge lengths and angles.

Regarding its vertices, notice that the two opposite faces, let’s say the front and back, have four of them each. So as it has two faces, there are in total eight vertices. To calculate them we can consider the number of sides of the bases and multiply them by three.

The number of edges that a prism has, can be also determined multiplying the number of sides of the bases by 3, which in the case of this geometric shape will give a total of twelve.

The surface area of a rectangular prism 

Given the above, it is now easy to understand how the surface area of this solid is computed.

The surface area is the sum of the areas of its six sides. Please consider that the opposite sides have the same surface. To find it, it will be necessary:

  • Find the area of two sides using: (length x height) x 2 sides
  • Find the area of the adjacent sides using: (width x height) x 2 sides
  • Find the area of the ends using: (length x width) x 2 ends
  • Add the three resulting areas. The sum of them are the surface area.

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The surface area of a rectangular prism 

Finally, as it is a solid body, it is possible to determine its volume by multiplying the length x width x height.

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