In Geometry, we have studied various three-dimensional shapes which are also known as solid shapes or solids. Some examples are cubes, cuboid, cylinder, prism, sphere, hemisphere, and so on. In this article, we are going to focus on the square prism definition, types, surface area and volume formulas.
Square prism Definition
A square prism is a three-dimensional shape cuboid figure whose bases are squares. The opposite sides and angles are congruent to each other. In the given figure, the bases of the prism are square, and therefore, it is called a square prism.
Types of Square prism
Square prisms are of two types. They are:
Right Square Prism
A prism with square bases is called a square prism. If the lateral faces of a square prism are perpendicular to its base, then it is referred to as the right square prism
- Vertices of a square prism = 8
- Edges of a square prism = 12
- Faces of a square prism= 6 (including bases)
Oblique Square Prism
If the bases of a square prism are not perpendicular to each other, then it is known as an oblique prism.
Properties of Square prism
Some important properties of the square prism are:
- Opposite sides are parallel to each other
- Opposite sides are congruent to each other
- Opposite angles are congruent to each other
- Diagonals bisect each other
- Consecutive angles are supplementary
Square Prism Formulas
The formulas to find the surface area and the volume are as follows:
Surface Area of a Square Prism
The surface area of a square prism is the measure of the total area of a surface of a three-dimensional solid object. It is expressed in square units. The surface area of a prism is defined as the sum of twice the base area and the lateral surface area of the prism.
The surface area of a square prism formula is given as,
The surface area of the square prism, SA = 2a^{2} + 4ah square units
Where
a is the side of the square prism
h is the height of the square prism
Volume of a Square prism
The volume of a square prism is a measurement of the occupied units of the solid. The volume of a square prism is the number of units used to fill a cube. It is represented by cubic units. The volume of a square prism formula is as follows,
The volume of a square Prism = Area of base × Height of the prism
If “a” is the side of the base, and “h” is the height of the prism, then
The Volume a Square Prism, V = a^{2} h cubic units.
Square Prism Example
Question:
Find the surface area and the volume of a square prism whose side is 3 cm and height is 5 cm.
Solution:
Given:
Side, a = 3 cm
Height, h = 5 cm
The surface area of the square prism, SA = 2a^{2} + 4ah square units
Now, substitute the given values
SA = 2(3)^{2} + 4(3)(5) cm^{2}
SA = 2(9) + 4(15) cm^{2}
SA = 18 + 60 cm^{2}
SA = 78 cm^{2}
Therefore, the surface area of a square prism is 78 cm^{2}
The Volume a Square Prism, V = a^{2} h cubic units.
V = (3)^{2} (5)
V = 9 (5)
V = 45 cm^{3}
Therefore, the volume of a square prism is 45 cm^{2}.
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