The Surface Area of a Rectangular Prism
Prisms are solid bodies that possess flat parallelogram sides with identical polygon ends. Thus prism can also be defined as a polyhedron that has two parallel polygonal bases that are facing each other. Therefore a rectangular prism is one that has two parallel bases that are rectangular in shape with four rectangular faces is known as a rectangular prism. The prism is not only rectangular in shape but it can also be a triangular, square, pentagonal and hexagonal prism. Thus the surface area of the rectangular prism is the sum of the parallel bases and the four lateral rectangular surfaces of the prism. Thus this article deals with the surface area of rectangular prism formula, its concepts, the method of calculating the rectangular prism area formula and the concept of the lateral area of a rectangular prism.
Surface Area of a Rectangular Prism Formula
Total region or the area covered by a rectangular prism that has all the six sides that are rectangular in shape with two parallel bases and four lateral rectangular surfaces. A rectangular prism has a three-dimensional structure for example a book or a matchstick or an aquarium. A right rectangular prism is also classified into two categories, namely, a right rectangular prism and an oblique rectangular prism. The difference between the two rectangular prisms is that in a right rectangular prism the base of a rectangular prism is perpendicular with another base whereas in an oblique rectangular prism the bases are not aligned on the top of each other equally. Thus in order to find the area of rectangular prism, we need to find the summation of all the areas of all the faces of the rectangular prism. Thus the rectangular prism has two types of areas.
Total surface area
Lateral surface area
The Total Surface Area of a Rectangular Prism
The total surface area of the rectangular prism is the sum of the areas of all the six surfaces of the prism. Thus the surface area of a rectangular prism formula is expressed as follows:-
Total surface area of a rectangular prism = 2(lb + bh + lh)
Where, l = length of the rectangular prism
b = breadth of the rectangular prism
h = height of the rectangular prism
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Solved Example of a Rectangular Prism
Find the total surface area of the rectangular prism using the surface area of rectangular prism whose length is 12cm, breadth is 6 cm and height is 4 cm.
Ans. according to the surface area of a prism formula = 2(lb + bh + lh)
= 2(12 x 6 + 6 x 4 + 12 x 4)
= 2 x 144 = 288 cm2
Lateral Surface Area of a Rectangular Prism
The lateral surface area of a rectangular prism can be calculated by adding all its lateral surfaces that are the four rectangular surfaces of the prism excluding the two bases of the prism. Thus surface area of a prism formula is expressed as follows:
Surface area of a prism = 2 (l + b) x h
Where, l = length of the rectangular prism
b = breadth of the rectangular prism
h = height of the rectangular prism
Find the lateral surface area of the rectangular prism using the surface area of a prism formula whose length is 12cm, breadth is 6 cm and height is 4 cm.
Formula surface area of prism for lateral surfaces = 2 (l + b) x h
= 2( 12 + 6) x 4
= 2 x 18 x 4 = 144 cm2
Solved Example of The Surface Area of A Rectangular Prism Formula
The total surface area of the prism is 70 ft2 with a base area of 10ft2 and the parameter of the rectangular prism is 14 ft. Thus by using the total surface area formula calculate the height of the rectangular prism.
Ans. Let us suppose that the length, breadth and height of the rectangular prism are l, b, h respectively. Thus from the above-given information, it is clear that the base area is calculated as lb = 10ft2. Also at the perimeter of the area of the base is given thus we know the base perimeter of the base = 2 (l + b) = 2l +2b = 14 ft
Thus using the total surface area of a prism we get:-
2(lb + bh + lh) = 70 ft2
= 2lb + 2(l + b) h = 70
= 2 x 10 + 14 x h = 70
= 20 + 14 h =70
= 14h = 70 -20 = 50
Or, h = 50 / 14 = 3.57 ft
Therefore the height of the rectangular prism is 3.57 ft.
FAQs on Surface Area of a Rectangular Prism Formula
1. Define the Lateral Surface Area of a Prism.
Ans. The lateral surfaces are all the surfaces that are present in a prism excluding the base of the prism. Thus as a rectangular prism consists of six surfaces among which two are the case, therefore, the total number of the lateral surface area of a rectangular prism is four.
2. What are the Examples of a Rectangular Prism?
Ans. A rectangular prism is a three-dimensional structure with six faces and has a length, breadth and height, thus, there are many real-life examples of rectangular prisms such as school notebooks, cuboidal fish aquariums, matchboxes and large structures such as storage rooms or cargo containers etc.
