Surface Area of a Square Prism
Let us start with the pre-required knowledge to understand the topic surface area of a square prism. A square prism (right square prism) is a prism having four sides as a rectangle and two squares as its bases (one square acts as the top). It is also known as a square cuboid or square box. It's a four-sided prism where the base and top are equal squares and the remaining 4 sides are rectangles. Both of the squares are parallel and congruent to each other. The rectangles are also congruent to each other.
In this section, we will discuss the surface area of a square prism along with solved examples.
| 1. | What Is Surface Area of a Square Prism? |
| 2. | Surface Area of a Square Prism Formula |
| 3. | How to Find Surface Area of a Square Prism? |
| 4. | FAQs on Surface Area of Square Prism |
What Is Surface Area of a Square Prism?
The surface area of a square prism is defined as the total region covered by the surfaces of a square prism. A square prism has four rectangular-shaped sides and two square bases. The surface area of a square prism is expressed in square units, common units being square meters, square centimeters, square inches, etc. Just like other three-dimensional shapes, a square prism also has two types of areas,
- Total Surface Area (TSA)
- Lateral Surface Area (LSA)
Let us understand the formulas to calculate both the lateral and total surface area of a square prism in the following section.
Surface Area of a Square Prism Formula
The surface area of a square prism is the sum of the areas of its faces and its base. We know that a square prism has:
So, the surface area of a square prism is the sum of the areas of four of its rectangular side faces and the base area which are squares.
Base Area of a Square Prism
For a square prism, if the length of the side of the square base is given, then its base area can be given by,
Base area of a square prism = Area of base square = s2, where, 's' is the length of the side of the base square.
Lateral Surface Area of a Square Prism
For a square prism, if the length of the side of the square and height of the prism is given, then its lateral surface area can be given by,
The lateral surface area of a square prism = Area of the four rectangular sides. Since all 4 rectangles are congruent, their areas will be equal.
Surface area of a square prism = 4 × (s × h) = 4sh, where, s is the length of the side of the square and h is the height of the square prism.
Total Surface Area of a Square Prism
For a square prism, if the length of the side of the square and height of the prism is given, then its total surface area can be given by:-
The total surface area of a square prism = 2 × Base Area + Lateral Surface Area
Total surface area of a square prism = 2 × s2 + 4 × (s × h) = 2s2 + 4sh, where, s is the length of the side of the square and h is the height of the square prism.
How to Find Surface Area of a Square Prism?
The following steps are used to calculate the surface area of a square prism :
- Step 1: Find the area of the square bases: 2s2, 's' is the base length.
- Step 2: Find the area of the four rectangular faces: The area of the four rectangular side faces can be given as 4sh, where, s is the length of the side of the square and h is the height of the square prism.
- Step 3: Add all the areas together for the total surface area of a square prism, while the area of 4 rectangular faces gives the lateral area of the square prism. Thus, the total surface area of a square prism is 2s2 + 4sh.
Thus, the total surface area of a square prism is 2s2 + 4sh and the lateral surface area is 4sh in squared units. Now, that we have seen the formula and method to calculate the surface area of a square prism, let us have a look at a few solved examples to understand it better.
FAQs on the Surface Area of a Square Prism
What Is Surface Area of a Square Prism?
Surface area of square prism is the area or region covered by the surfaces of the three-dimensional shape. A square prism has 2 square-shaped bases and 4 rectangular-shaped lateral faces. A square prism has two types of areas: lateral surface area and total surface area.
What Is the Formula to Calculate the Surface Area of a Square Prism?
The formula used to calculate the total surface area of a square prism is given as, TSA of a square prism = 2 × s2 + 4 × (s × h) = 2s2 + 4sh, where, s is the length of the side of the square and h is the height of the square prism. While the formula to calculate the lateral surface area of a square prism is given as, LSA of square prism = 4sh, where s is the length of the side of the square and h is the height of the square prism.
How to Calculate the Surface Area of a Square Prism?
To calculate the surface area of a square prism we can follow the steps given below,
- Step 1: Note down the dimensions of the square prism and figure out whether to calculate the lateral or total surface area according to the given condition.
- Step 2: Apply the formulas for LSA or TSA(as required in the question):
TSA of a square prism = 2 × s2 + 4 × (s × h) = 2s2 + 4sh
LSA of square prism = 4sh, where, s is the length of the side of the square and h is the height of the square prism. - Step 3: Express the answer in square units.
What Is the Lateral Surface Area of a Square Prism?
The lateral surface area of a square prism is the area covered by the lateral or side faces of the square prism. The lateral surface area can be calculated using the given formula, LSA of square prism = 4sh, where, s is the length of the side of the square and h is the height of the square prism.
What Are the Units Used To Express Surface Area of a Square Prism?
The total surface area of a square prism is expressed in square units. The common units used are square meters, square centimeters, square inches, square yards, etc.
How Do You Find the Height of a Square Prism When Given the Surface Area?
The surface area of a square prism is given by the formula: TSA of a square prism = 2 × s2 + 4 × (s × h) = 2s2 + 4sh, where, s is the length of the side of the square and h is the height of the square prism. Given the surface area and side length of the base square, we can substitute the known values in the formula, and solve for height.
What Is the Difference Between Lateral Surface Area and Total Surface Area of a Square Prism?
The lateral surface area of a square prism is the area covered by the lateral or side surfaces, while the total surface area of a square prism is the area covered by all the faces, including the two square bases.