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Calculating the surface area of a rectangle is an essential skill in mathematics and everyday life. Whether you are a student trying to solve a geometry problem or a homeowner measuring the amount of paint needed for a room, understanding how to find the surface area of a rectangle is crucial. This concept involves finding the total area of all sides of a rectangular shape, which is used to determine the amount of material required or to solve a variety of real-world problems. In this guide, we will explore a step-by-step approach to calculating the surface area of a rectangle, enabling you to confidently tackle any related task.
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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
- 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.
- There is one top and one bottom. These two sides are the same size. [1] X Research 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] X Research Source
- Going back to the example above, the area of the base is 4 cm x 3 cm = 12 square cm .
- Thus, the area of the top surface is also equal to 12 square centimeters .
- 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 .
- 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 .
- So the area of the rectangular box in the given example is: 12 + 12 + 15 + 15 + 20 + 20 = 94 square centimeters .
Shorten the Formula
- Area of rectangular box = 2lw + 2wh + 2lh
- Area of rectangular box = 2lw + 2wh + 2lh = 2(lw + wh + lh) .
- 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] X Research 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] X Research 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 straightforward process that requires only a few simple steps. By correctly measuring the length and width of the rectangle, multiplying these two values together, and then multiplying the result by 2, one can easily determine the total surface area of the rectangle. It is important to remember that surface area is expressed in square units, as it represents the total area covered by the outer faces of the rectangle. This calculation can be valuable in various fields such as architecture, engineering, and construction, as it helps determine material requirements and space utilization. The ability to calculate surface area is a fundamental skill that is beneficial to anyone working with rectangular objects or structures.
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