Calculating the Surface Area of a Rectangular Prism: A Step-by-Step Guide

Understanding how to find the surface area of a rectangular prism is an essential skill in geometry. This tutorial will provide a detailed step-by-step guide to calculating the surface area of a rectangular prism with dimensions given in different units. We will also solve a specific example to illustrate the process.

Understanding Rectangular Prisms and Surface Area

A rectangular prism is a three-dimensional shape with six faces, all of which are rectangles. The surface area of a rectangular prism is the total area of all its faces combined. It is a measure of the total area that the surface of the prism occupies.

Example: Calculating the Surface Area

Consider a rectangular prism with a length of 12 cm, a width of 90 cm, and a height of 0.1 m. The first step is to ensure all dimensions are in the same unit. Since 0.1 m is equal to 10 cm, we can convert the height to centimeters.

Step 1: Convert Units

Height: 0.1 m 10 cm

Step 2: Calculate the Area of Each Face

A rectangular prism has six faces, with pairs of opposite faces being congruent. The areas of the faces are calculated as follows:

Front and Back Faces (length x height): 12 cm x 10 cm 120 cm2 Left and Right Faces (width x height): 90 cm x 10 cm 900 cm2 Top and Bottom Faces (length x width): 12 cm x 90 cm 1080 cm2

Step 3: Sum the Areas of All Faces

The sum of the areas of all faces is: Front and Back Faces: 2 x 120 cm2 240 cm2 Left and Right Faces: 2 x 900 cm2 1800 cm2 Top and Bottom Faces: 2 x 1080 cm2 2160 cm2

Total Surface Area 240 cm2 1800 cm2 2160 cm2 4200 cm2

Visualizing the Solution

Visualization can help in understanding the concept better. Imagine a rectangular prism with the dimensions 12 cm x 90 cm x 10 cm. The front and back faces would each have an area of 120 cm2, the left and right faces would each have an area of 900 cm2, and the top and bottom faces would each have an area of 1080 cm2.

Practical Applications and Importance

Understanding how to calculate the surface area of a rectangular prism is not only important for academic purposes but also for various practical applications such as:

Building materials estimation Painting and coating requirements Package design and printing

Conclusion

By following these steps, you can easily calculate the surface area of a rectangular prism. This skill is valuable in many real-world scenarios and can enhance your problem-solving abilities in mathematics and related fields.

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