Formula for Total Surface Area of Rectangular Prism & Examples

This article guides you through the formula for calculating the total surface area of a rectangular prism along with some illustrative examples for practice.

1. Overview of Rectangular Prism

Definition

Rectangular prism is recognized as a type of spatial figure with a total of 6 faces, all of which are rectangles. The opposite faces of the rectangular prism are considered as the two base faces. The remaining faces are the lateral faces of the rectangular prism.

Properties:

• The area of two opposite faces in a rectangular prism will be equal.
• The perimeter of two opposite faces in a rectangular prism will be equal.
• A rectangular prism will have a total of 12 edges, 8 vertices, and 6 faces.
• The diagonals in a rectangular prism have their endpoints at 2 opposite vertices of the rectangular prism, converging at a specific point.

2. Formula for Calculating Total Surface Area of Rectangular Prism

Formula for Total Surface Area:

S_TP = S_XY + 2.a.b = 2.h.(a + b) + 2.a.b

+ Stated in words: The total surface area of a rectangular prism equals the sum of its lateral surface area and 2 remaining faces of the prism.

- Explanation of symbols in the total surface area formula:

• S_xy represents the lateral surface area of the rectangular prism
• S_TP represents the total surface area of the rectangular prism
• a, b respectively denote the length and width of the rectangular prism
• h denotes the height of the rectangular prism

- Unit of measurement for the surface area of the rectangular prism: square meters (m²)

Example: Given a classroom shaped like a rectangular prism with a length of 8m, width of 4m, and height of 5m. What is the total surface area of this room?

Solution:

The lateral surface area of that classroom is:

2 x 5 x (8 + 4) = 120(m²)

The total area of the two bases of that classroom is:

2 x 8 x 4 = 64(m²)

The total surface area of that classroom is:

120 + 64= 184 (m²)

Answer: 184 m²

3. Types of problems involving total surface area of rectangular prisms

Type 1: Calculate the total surface area of a rectangular prism

Method for solving this type of problem: Apply the rule for calculating the total surface area of a rectangular prism.

Type 2: Given the total surface area, find the perimeter of the base or calculate the height of a rectangular prism.

Method for solving this type of problem:

- From the formula S_tp = S_xq + 2.a.b = 2.h.(a + b) + 2.a.b

- Find the height h using the formula: h = [S_tp- 2.a.b] : (2.a + 2.b)

- Find the total perimeter of the base using the formula: (a + b). 2 = [S_tp- 2.a.b] : h.

Type 3: Word problem type (often involves finding the area of a box, room, painting walls, etc.)

Method: Determine whether the area to find is the lateral surface area or the total surface area, then apply the rule for calculating either the lateral surface area or the total surface area in the problem.

This article has addressed the formula for calculating the total surface area of a rectangular prism & Examples. Have a great day!