PRISM

A prism is a solid shape that is bound on all its sides by plane faces. There are two types of faces in a prism. The top and bottom faces are identical and are called bases. A prism is named after the shape of these bases. For example, if a prism has a triangular base it is called a triangular prism.

The faces other than the top and bottom of a prism are called its lateral faces. All the lateral faces are also identical to each other and belong to the class of parallelograms. This means that the lateral faces can either be parallelograms, rectangles, or even squares since all of them have their opposite sides parallel to each other. One of the most common examples of a prism is a cuboid. It has a rectangular base and is called a rectangular prism.

Based on the shape of the base, prisms can be categorized into the following:

• Triangular prism: The base of the prism is triangular in shape.
  
• Hexagonal prism: It is a prism with a base in the shape of a hexagon.
  

• Square prism: A prism that has a base in the shape of a square. You may have seen a square prism with a different name, it is also called a cube.
  

• Pentagonal prism: The base of the prism is shaped like a pentagon.
  

• Rectangular prism: A prism that has bases in the shape of a rectangle. A rectangular prism is also known as a cuboid.
  

QUERY 1

The base of a solid right prism is a triangle whose sides are 9 cm, 12 cm, 15 cm. The height of the prism is 5 cm, find total surface area of the prism.

A) 188
B) 200
C) 155
D) 288

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Total surface area of a prism = (perimeter of triangle at its base*height) + 2area of its base

Now the perimeter of the base = 9 + 12 + 15 = 36
And area of the base = 9*12/2 = 54 (as the base of the prism is a right triangle; we can easily make it out that 9 and 12 should be the combination of it’s height and base)

Thus the total surface area of the prism = (36*5) + 2*54
= 288 (option ‘D’)

QUERY 2

Calculate the volume of a prism with a height of 7 cm and an area of the base of 60 cm².

MAHA GUPTA
Volume of prism = Area of base ✕ Height
Here, Height = 7 cm and Area of base = 60 cm²
Therefore, the volume of the given prism = 60 ✕ 7 = 420 cm³

QUERY 3

Calculate the surface area of a prism with a base area of 25 cm², a base perimeter of 24 cm, and a height of 10 cm.

MAHA GUPTA
Surface Area of a prism = (2Base Area) + (Base perimeter ✕ Height)
Here, Height = 10 cm and Area of base = 25 cm² and Perimeter of base = 24 cm
Therefore, the surface area of the given prism = (2*25) + (24*10) = 50 + 240 = 290 cm²

QUERY 4

Find out the volume of a prism with a base area of 25 cm² and length of 12 cm.

MAHA GUPTA
Volume of prism = Area of base ✕ Height
Here, Height = 12 cm and Area of base = 25 cm²
Therefore, the volume of the given prism = 25*12 = 300 cm³

QUERY 5

Find the volume of a triangular prism whose area is 60 cm² and height is 7 cm.

MAHA GUPTA
Volume of a prism = (Base area × Height)
Therefore, V = 60 ×7 = 420
Hence, the volume of a triangular prism = 420 cm³

QUERY 6

Find the height of the square prism whose volume is 360 cm³ and the base area is 60 cm².

MAHA GUPTA
Volume of square prism = Base area × height
Therefore, the height, h = 360/60
Prism Height, h = 6 cm.