A prism is a three-dimensional soild object having two identical and parallel shapes facing each other. The identical shapes are called the bases. The bases can have any shape of a polygon such as triangles, square, rectangle, or a pentagon. The diagram below shows a triangular prism.
Prism
Definition
A prism is a member of the polyhedron family consisting of two identical and parallel polygonal bases. The bases are connected by flat faces forming a uniform cross-section.
In general, a prism refers to a transparent solid used to refract or scatter a beam of white light. It is a commonly used instrument in physics.
Parts
A prism has bases, lateral faces, edges, and vertices.
Prism Parts
Base – The parallel faces which makes the 2 ends of any prism. They are congruent. The base determines the cross-section of any prism and it remains uniform throughout the shape.
Lateral faces – The non-parallel faces which connects the 2 bases.
A prism can also be classified into regular or irregular based on the uniformity of its cross-section. It can be right or oblique, depending on the alignment of its bases.
Regular and Irregular Prisms
The diagram shows the difference between a regular and irregular triangular prism.
Regular vs Irregular Prisms
Regular Prism – It has a base which is a regular polygon with equal side lengths. Regular prisms have identical bases and identical lateral faces. Thus, all the above examples of prisms are regular such as triangular, rectangular, and pentagonal.
Irregular Prism – It has a base which is an irregular polygon with unequal side lengths. Irregular prisms have identical bases. However, the lateral faces are not identical.
Right and Oblique Prisms
The diagram shows the difference between a right and an oblique pentagonal prism.
Right vs Oblique Prism
Right Prism – Its lateral faces are perpendicular to its bases. The 2 bases of a right prism is aligned perfectly over one another.
Oblique Prism– It is a slanted prism. So its lateral faces are not perpendicular to its bases. The 2 bases are not aligned perfectly over one another.
Like all other polyhedrons, a prism also has a surface area and a volume.
Formulas
Surface Area
Lateral Surface Area (LSA) = Perimeter × Height
Total Surface Area (TSA) = (2 × Base Area) + LSA
∴TSA= (2 × Base Area) + (Perimeter × Height)
here, height is the distance between the 2 bases or the length of the prism.
Volume
Volume = Base Area × Height, here, height is the distance between the 2 bases or the length of the prism.
Let us solve some examples involving prisms and the above formulas
Solved Examples
Find the surface area of a triangular prism given whose base area is 12 cm2, perimeter is 16 cm, and length is 7 cm.
Solution:
As we know, Total Surface Area (TSA) = (2 × Base Area) + (Perimeter × Height), here base Area = 12 cm2, perimeter = 16 cm, height = length = 7 cm ∴ TSA = (2 × 12) + (16 × 7) = 136 in2
Find the total and lateral surface area of a rectangular prism whose base area is 36 cm2 , perimeter is 30 cm, and height is 11 cm.
Solution:
As we know, Total Surface Area (TSA) = (2 × Base Area) + (Perimeter × Height), here base area = 36 cm2, perimeter = 30 cm, height = 11 cm ∴ TSA = (2 × 36) + (30 × 11) = 402 cm2 Lateral Surface Area (LSA) = Perimeter × Height ∴ LSA = 30 × 11 = 330 cm2
Find thevolume of a triangular prism whose base area is 64 cm2 and height is 7 cm.
Solution:
As we know, Volume (V) = Base Area × Height ∴ V= B × h, here B = 64 cm2, h = 7 cm = 64 × 7 = 448 cm3
Real-life Examples
Ice cubes and candy bars
Books and notebooks
A Rubik’s cube
Camping tents and barns
Glass or plastic prisms used in science laboratories to see spectrum of white light
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