Last updated on July 31st, 2025
A square prism, also known as a rectangular prism with a square base, is a 3-dimensional shape that has square bases. The surface area of a square prism is the total area covered by its outer surface. It includes the areas of the four rectangular faces and the two square bases. In this article, we will learn about the surface area of a square prism.
The surface area of a square prism is the total area occupied by the boundary or surface of the prism. It is measured in square units.
A square prism is a 3D shape with two parallel square bases and four rectangular faces connecting the bases.
The surface area of a square prism includes the area of the four rectangular faces and the two square bases. Square prisms are a type of rectangular prism where the bases are squares.
A square prism has two types of surface areas: the lateral surface area and the total surface area. Look at the square prism below to see its surface area, height(h), and side length(s) of the square base.
A square prism has two types of surface areas:
The lateral surface area of a square prism is the total area of the four rectangular faces, excluding the base areas.
The formula for the lateral surface area (LSA) of the square prism is given as:
Lateral Surface Area = 4sh square units
Here, s is the side length of the square base. h is the height of the prism.
The total area occupied by the square prism, including the area of the lateral surfaces and the area of the two square bases, is known as the total surface area of the square prism.
The total surface area of a square prism is calculated by using the formula: Total surface area = 2s² + 4sh square units Where s is the side length of the square base. h is the height of the prism.
Derivation of the Total Surface Area of a Square Prism
To find the total surface area of a square prism, consider its two square bases and four rectangular lateral faces.
Total surface area of a square prism = 2 × area of base + lateral surface area
Here, the area of the base = s² Lateral surface area = 4sh
Substituting the formulas into the total surface area, Total surface area of a square prism, T = 2s² + 4sh
The volume of a square prism shows how much space is inside it. It tells us how much it can hold. The volume of a square prism can be found by using the formula: Volume = s²h cubic units
Students assume that the lateral surface area (LSA) and the total surface area (TSA) of a square prism are the same. This confusion arises because both involve the side length and the height. Always remember that LSA is only for the lateral faces, and TSA includes both the lateral surfaces and the bases.
Given s = 5 cm, h = 10 cm. Use the formula: LSA = 4sh = 4 × 5 × 10 = 20 × 10 = 200 cm²
Find the total surface area of a square prism with side length 4 cm and height 7 cm.
TSA = 136 cm²
Use the formula: TSA = 2s² + 4sh = 2 × 4² + 4 × 4 × 7 = 2 × 16 + 112 = 32 + 112 = 144 cm²
A square prism has a side length of 6 cm and a height of 9 cm. Find the total surface area.
TSA = 234 cm²
Use the TSA formula: TSA = 2s² + 4sh = 2 × 6² + 4 × 6 × 9 = 2 × 36 + 216 = 72 + 216 = 288 cm²
Find the lateral surface area of a square prism with side length 3.5 cm and height 8 cm.
LSA = 112 cm²
LSA = 4sh = 4 × 3.5 × 8 = 14 × 8 = 112 cm²
The height of a square prism is 15 cm, and its lateral surface area is 300 cm². Find the side length.
Side length = 5 cm
Students often make mistakes while calculating the surface area of a square prism, which leads to wrong answers. Below are some common mistakes and the ways to avoid them.
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