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Calculating the surface area of a rectangle is a fundamental skill in mathematics and is often encountered in various fields, ranging from geometry to architecture and engineering. While a rectangle may seem like a simple shape, accurately determining its surface area requires a systematic approach and an understanding of the underlying principles. By following a set of formulas and steps, individuals can confidently calculate the surface area of a rectangle, enabling them to make informed decisions or solve mathematical problems involving this shape. In this guide, we will provide a comprehensive overview of the process of calculating the surface area of a rectangle, including the formulas involved and practical examples to illustrate the concept. Whether you are a student seeking to enhance your mathematical skills or an individual interested in practical applications of geometry, this guide will equip you with the necessary knowledge and tools to tackle this calculation with confidence.
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A rectangular box is a shape with 6 faces that people often call a box. Think of a brick, or a shoebox so you can figure out exactly what a rectangular box is. Surface area is the total area of the outer part of the object. “How much paper do I need to wrap this shoebox” sounds much less complicated, but it’s exactly the same math.
Steps
Find Surface Area
![Image titled Find the Surface Area of a Rectangular Prism Step 1](https://www.wikihow.com/images_en/thumb/e/e7/Find-the-Surface-Area-of-a-Rectangular-Prism-Step-1-Version-3.jpg/v4-728px-Find-the-Surface-Area-of-a-Rectangular-Prism-Step-1-Version-3.jpg)
- If you don’t know which edge to mark, choose any corner. Mark the three lines that intersect at that corner.
- Example: A box has a bottom of 3 cm x 4 cm, and a height of 5 cm. The long side of the base is 4 cm, so l = 4, w = 3, and h = 5.
![Image titled Find the Surface Area of a Rectangular Prism Step 2](https://www.wikihow.com/images_en/thumb/f/f9/Find-the-Surface-Area-of-a-Rectangular-Prism-Step-2-Version-3.jpg/v4-728px-Find-the-Surface-Area-of-a-Rectangular-Prism-Step-2-Version-3.jpg)
- There is one top and one bottom. These two sides are the same size. [1] XResearch Source
- There is one front and one back. These two sides are the same size.
- There is a left side and a right side. These two sides are the same size.
- If it’s hard to visualize, cut a paper box into sections along the edges and spread it out. [2] XResearch Source
![Image titled Find the Surface Area of a Rectangular Prism Step 3](https://www.wikihow.com/images_en/thumb/b/b1/Find-the-Surface-Area-of-a-Rectangular-Prism-Step-3-Version-3.jpg/v4-728px-Find-the-Surface-Area-of-a-Rectangular-Prism-Step-3-Version-3.jpg)
- Going back to the example above, the area of the base is 4 cm x 3 cm = 12 square cm .
![Image titled Find the Surface Area of a Rectangular Prism Step 4](https://www.wikihow.com/images_en/thumb/b/bc/Find-the-Surface-Area-of-a-Rectangular-Prism-Step-4-Version-3.jpg/v4-728px-Find-the-Surface-Area-of-a-Rectangular-Prism-Step-4-Version-3.jpg)
- Thus, the area of the top surface is also equal to 12 square centimeters .
![Image titled Find the Surface Area of a Rectangular Prism Step 5](https://www.wikihow.com/images_en/thumb/1/11/Find-the-Surface-Area-of-a-Rectangular-Prism-Step-5-Version-3.jpg/v4-728px-Find-the-Surface-Area-of-a-Rectangular-Prism-Step-5-Version-3.jpg)
- In the above example, w = 3 cm and h = 5 cm, so the frontal area is 3 cm x 5 cm = 15 square cm . The area of the back is also equal to 15 square centimeters .
![Image titled Find the Surface Area of a Rectangular Prism Step 6](https://www.wikihow.com/images_en/thumb/a/ac/Find-the-Surface-Area-of-a-Rectangular-Prism-Step-6-Version-3.jpg/v4-728px-Find-the-Surface-Area-of-a-Rectangular-Prism-Step-6-Version-3.jpg)
- In the above example, l = 4 cm and h = 5 cm, so the area of the reverse side = 4 cm x 5 cm = 20 square cm . The area of the right face is also equal to 20 square centimeters .
![Image titled Find the Surface Area of a Rectangular Prism Step 7](https://www.wikihow.com/images_en/thumb/9/98/Find-the-Surface-Area-of-a-Rectangular-Prism-Step-7-Version-3.jpg/v4-728px-Find-the-Surface-Area-of-a-Rectangular-Prism-Step-7-Version-3.jpg)
- So the area of the rectangular box in the given example is: 12 + 12 + 15 + 15 + 20 + 20 = 94 square centimeters .
Shorten the Formula
![Image titled Find the Surface Area of a Rectangular Prism Step 8](https://www.wikihow.com/images_en/thumb/e/e8/Find-the-Surface-Area-of-a-Rectangular-Prism-Step-8-Version-3.jpg/v4-728px-Find-the-Surface-Area-of-a-Rectangular-Prism-Step-8-Version-3.jpg)
- Area of rectangular box = 2lw + 2wh + 2lh
![Image titled Find the Surface Area of a Rectangular Prism Step 9](https://www.wikihow.com/images_en/thumb/2/25/Find-the-Surface-Area-of-a-Rectangular-Prism-Step-9-Version-3.jpg/v4-728px-Find-the-Surface-Area-of-a-Rectangular-Prism-Step-9-Version-3.jpg)
- Area of rectangular box = 2lw + 2wh + 2lh = 2(lw + wh + lh) .
![Image titled Find the Surface Area of a Rectangular Prism Step 10](https://www.wikihow.com/images_en/thumb/2/2d/Find-the-Surface-Area-of-a-Rectangular-Prism-Step-10-Version-3.jpg/v4-728px-Find-the-Surface-Area-of-a-Rectangular-Prism-Step-10-Version-3.jpg)
- Area = 2(lw + wh + lh) = 2 x (lw + wh + lh) = 2 x (4×3 + 3×5 + 4×5) = 2 x (12 + 15 + 20) = 2 x (47) = 94 cm square. The result is the same as the original, but this calculation is much faster.
Advice
- Always use “square units”, like square centimeters or square meters. [3] XResearch Sources . If a box has a surface area of 50 square meters, that means that 50 square meters is needed to cover the entire surface of the box.
- Some teachers use “width” or “thickness” instead of the above names. This doesn’t matter as long as you name each edge explicitly.
- If you don’t know what the height of the box is, you can call any side the height. The length is usually the longest side, but even that doesn’t really matter. It is important that the name you choose is consistent throughout the problem. [4] XResearch Sources
wikiHow is a “wiki” site, which means that many of the articles here are written by multiple authors. To create this article, 55 people, some of whom are anonymous, have edited and improved the article over time.
This article has been viewed 72,719 times.
A rectangular box is a shape with 6 faces that people often call a box. Think of a brick, or a shoebox so you can figure out exactly what a rectangular box is. Surface area is the total area of the outer part of the object. “How much paper do I need to wrap this shoebox” sounds much less complicated, but it’s exactly the same math.
In conclusion, calculating the surface area of a rectangle is a relatively simple process that involves understanding the formula and proper measurements. By multiplying the length and width of the rectangle, you can determine the area of each face. Then, by adding these areas together, you can find the total surface area of the rectangle. The surface area of a rectangle is an important calculation in various fields such as construction, architecture, and engineering. Mastering this calculation is essential for accurately estimating material requirements and costs. Overall, understanding how to calculate the surface area of a rectangle is a valuable skill that can be applied in many real-life scenarios.
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