The Right Way to Calculate the Surface Area of Rectangular Prism

A rectangular prism popularly known as a cuboid is a 3-D geometric shape with six rectangular faces. As all the faces are in the shape of a rectangle, every opposite side is equal. Both the top and bottom of this prism are in the shape of a rectangle. One can easily locate these in our daily life such as laptops, books, aquariums, etc. A rectangular prism is of two types i.e. right rectangular prism and an oblique rectangular prism. Under the former one, the side faces are perpendicular to one another whereas in the case of the latter all the side faces are in the shape of a parallelogram. Mostly when there is no description of a rectangular prism, we consider it the right rectangular prism. The rectangular prism consists of three dimensions namely length, breadth, and height. All these dimensions are used in the calculation of the surface area of rectangular prism.

The surface area of the rectangular prism is known as the total surface that is occupied by all its rectangular faces. In total there are six faces of the rectangular prism. The surface area of a rectangular prism can be used for various purposes such as the wrapping of a box. To know about the amount of paper needed for wrapping one needs to know about all the areas of the surface i.e. lateral, top as well as bottom surface. The total calculation of area will help you to arrive at the surface area of the rectangular prism. The surface area of a rectangular prism is to be represented in square units.

A rectangular surface area is of two types and thus both have different formulas that are used to arrive at its calculations. These are known as the total surface and the lateral surface area.

  • The formula for the total surface area: Total surface area of the rectangular prism is nothing but the sum of all the rectangular six faces of the prism.

TSA of rectangular prism = 2(lb+bh+hl)

Where l, b, h represents the length, breadth, and height of the rectangular prism respectively.

  • The formula for the lateral surface area: To calculate the lateral surface area of the rectangular prism the area of lateral surfaces is to be taken into consideration. Thus the lateral surface area represents the total area but minus the area of the base.

LSA of rectangular prism= 2(l+b) h

Where l, b, h represents the length, breadth, and height of the rectangular prism respectively.

With the above formula, anyone can easily calculate the surface area of the rectangular prism whether total or lateral. Besides the surface area, the volume of the rectangular prism is another important calculation. It is done by multiplying all three dimensions i.e. length, breadth, and height. In case that all the sides of the rectangular prism are same then it is nothing but a cube and thereby all the formulas of the cube apply to it.

To avoid any error, one must calculate the surface area of the prism of the rectangular shapes using the help of the following steps. These include:

  • The first thing to be done is to ensure that all three dimensions i.e. length, breadth and the height of the prism are in the similar units. If they are not then one must convert them first before moving to the next step.
  • Once the conversion is done into the same units, then as per the problem or situation, see whether the calculation of the total surface is required or the lateral surface.
  • After determining which surface area is to be applied, the next step is to apply the right formula for respective calculations.
  • Once the required surface area is calculated one must not forget to denominate it in terms of square units.

Hence with this detailed method, the calculation of surface area is no more a headache. To completely master it one must practice these as much as possible and that too from the quality source which is none other than Cuemath. It will help in clearing all your doubts.

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