Square prism
A square prism is a three-dimensional cuboid in which the bases are squares. It has six faces in which two opposite faces are square in shape while the other four are rectangular. It should be noted that all square prisms are not cubes but all cubes are square prisms because cubes fulfill the properties of square prisms. Let us understand more about square prisms.
| 1. | Definition of a Square Prism |
| 2. | Properties of Square Prisms |
| 3. | Types of Square Prisms |
| 4. | Square Prism Formulas |
| 5. | Square Prism Net |
| 6. | FAQs on Square Prism |
Definition of a Square Prism
A square prism is a three-dimensional cuboid where the base and top are equal squares and the remaining 4 faces are rectangles. The opposite sides and angles of a square prism are congruent and parallel to each other. A square prism has at least two of its length equal to each other. A real-life example is a tissue box that we see in our daily life.
Properties of Square Prism
A square prism has two ends as faces shaped like a square with 4 rectangles or squares in between them as other faces. Let us look at the various properties of a square prism:
- A square prism has 6 faces, 8 vertices, and 12 edges.
- The opposite sides of a square prism are parallel to each other.
- The opposite sides of a square prism are congruent to each other.
- In a square prism, the diagonals bisect each other.
- In a square prism, opposite angles are congruent to each other.
Types of Square Prisms
A square prism can be classified into two types. Let us learn the types in detail.
Right Square Prism
If the lateral faces of a square prism are aligned in one direction to its base, then it is termed as a right square prism. In other words, if the lateral faces are perpendicular to the base of the prism then the prism is a right square prism.
Oblique Square Prism
If the lateral faces of a prism are not perpendicular to the base of the prism, then it is known as an oblique square prism. Observe the following figure to note the difference between a right square prism and an oblique square prism.
Square Prism Formulas
There are two basic formulas related to the square prism:
- Surface area of a square prism.
- Volume of a square prism.
Surface area of square prism: If the length of the side of the square and height of a square prism is given, then its total surface area can be calculated with the help of the following formulas:
- The total surface area of a square prism = (2 × Base Area) + Lateral Surface Area
- This can be written as: (2 × a2) + (4 × a × h) = 2a2 + 4ah (where 'a' is the length of the side of the square and 'h' is the height of the square prism.)
Volume of a square prism: The amount of space occupied by a 3-dimensional prism is known as its volume and it is measured in cubic units.
- The volume of a prism is its cross-sectional area multiplied by its length. In other words, the volume of a square prism is its base area multiplied by its height.
- This can be written as: a2 h (where, a = side of a square prism, a2 = base area, h = height of the square prism)
Square Prism Net
A square prism net is when the solid shape is flattened by opening the prism entirely. The view of the square prism net provided us the accurate shapes of the 2 square faces along with 4 rectangle faces. When all flattened ends are combined together, we get the shape of a square prism. The image below shows the net of the square prism.
Related Articles on Square Prism
Check out the important topics mentioned below to learn more about square prism and its related terminologies.
FAQs on Square Prism
Is a Square Prism the Same as a Cube? Explain.
No, all square prisms are not the same as cubes. A square prism is a three-dimensional solid figure with six faces in which the two opposite faces are squares while the other four are rectangular. A cube is a three-dimensional solid figure with all its faces as squares. Therefore, all cubes can be square prisms, but all square prisms cannot be cubes.
What is the Square Prism Formula?
There are two basic formulas related to a square prism:
- Surface Area of a square prism = 2a2 + 4ah
- Volume of a square prism = a2h
Here, a = the length of the side of the prism; and h = the height of the prism
What are the Properties of a Square Prism?
The basic properties of a square prism are as follows:
- In a square prism, the opposite sides are parallel and congruent to each other.
- The opposite angles of a square prism are congruent to each other.
- The sum of the consecutive angles of a square prism is supplementary, that is, 180°.
What is a Square Prism?
A three dimensional cuboid with six faces in which the bases are squares, is identified as a square prism. In a square prism, the opposite sides and angles are congruent to each other.
How Many Vertices, Edges, and Faces Does a Square Prism Have?
A square prism has 8 vertices, 12 edges, and 6 faces.
What is the Volume of a Square Prism?
The volume of a square prism is the product of its base area and height. If the length of the side of the base square and the height of the prism is given, then its volume can be calculated using the following formula: Volume = Base Area × Height of the prism = s2 × h; where 's' is the length of the side of the base square and 'h' is the height of the prism.
What is a Truncated Square Prism?
A truncated square prism is a part of a prism which is formed by passing a plane which is not parallel to the base and which intersects all the lateral edges. In a truncated square prism the lateral edges are non-congruent and the lateral faces are quadrilaterals.
What is the Net of a Square Prism?
The net of a square prism is the flattened version of the solid. The square prism when opened showcases the squares and rectangles. When combined together, it becomes a square prism