The Surface Area Expression

Oct 13, 2025 by miodeya.com 28 views

Introduction

In mathematics, surface area calculations are crucial in various fields, including engineering, architecture, and design. The ability to accurately calculate surface areas is essential for determining the total surface area of objects, which can be used to estimate the amount of material required for construction or manufacturing. In this article, we will delve into a surface area calculation problem and identify the error made by Devon, a student who attempted to simplify the expression.

The Surface Area Expression

The surface area expression given to Devon is:

$2((9)(20)) + 2((9)(34)) + (34)(20) + 2\left(\frac{1}{2}(20)(24)\right) + 2\left(\frac{1}{2}(34)(26)\right)$

This expression represents the surface area of an object, and Devon's task is to simplify it.

Devon's Mistake

After analyzing the expression, we can see that Devon made a mistake by not correctly simplifying the expression. Let's break down the expression and identify the error.

Step 1: Simplify the Multiplication

The first step in simplifying the expression is to multiply the numbers inside the parentheses.

$2((9)(20)) = 2(180) = 360$

$2((9)(34)) = 2(306) = 612$

$(34)(20) = 680$

$\frac{1}{2}(20)(24) = 240$

$\frac{1}{2}(34)(26) = 442$

Step 2: Add the Terms

Now that we have simplified the multiplication, we can add the terms together.

$360 + 612 + 680 + 240 + 442 = 2034$

However, Devon's mistake was not in the calculation itself, but in the fact that he did not simplify the expression correctly.

The Correct Simplification

To simplify the expression correctly, we need to combine like terms and eliminate any unnecessary calculations.

$2((9)(20)) + 2((9)(34)) + (34)(20) + 2\left(\frac{1}{2}(20)(24)\right) + 2\left(\frac{1}{2}(34)(26)\right)$

$= 2(9)(20) + 2(9)(34) + (34)(20) + (20)(24) + (34)(26)$

$= 2(180) + 2(306) + 680 + 480 + 884$

$= 360 + 612 + 680 + 480 + 884$

$= 2416$

Conclusion

In conclusion, Devon's mistake was not in the calculation itself, but in the fact that he did not simplify the expression correctly. By combining like terms and eliminating unnecessary calculations, we can simplify the expression and arrive at the correct answer.

Discussion

A. He used 26 instead of 24 in the second to last term.

B. He did not simplify the expression correctly.

C. He used the wrong formula for surface area.

D. He did not calculate the expression correctly.

The correct answer is B. He did not simplify the expression correctly.

Final Answer

Introduction

In our previous article, we explored the surface area calculation problem that Devon attempted to solve. We identified the error in his calculation and provided the correct solution. In this article, we will answer some frequently asked questions related to surface area calculations and Devon's mistake.

Q: What is surface area, and why is it important?

A: Surface area is the total area of the surface of an object. It is an important concept in mathematics, engineering, and design, as it can be used to estimate the amount of material required for construction or manufacturing.

Q: What is the formula for surface area?

A: The formula for surface area depends on the shape of the object. For a rectangular prism, the surface area is given by:

SA = 2lw + 2lh + 2wh

where l, w, and h are the length, width, and height of the prism, respectively.

Q: What was Devon's mistake in the surface area calculation?

A: Devon's mistake was not in the calculation itself, but in the fact that he did not simplify the expression correctly. He failed to combine like terms and eliminate unnecessary calculations, which led to an incorrect answer.

Q: What is the correct answer to the surface area calculation?

A: The correct answer to the surface area calculation is 2416.

Q: Why is it important to simplify expressions correctly?

A: Simplifying expressions correctly is important because it helps to eliminate unnecessary calculations and ensures that the correct answer is obtained. Inaccurate calculations can lead to incorrect conclusions and decisions, which can have serious consequences in fields such as engineering and design.

Q: How can I avoid making mistakes like Devon's?

A: To avoid making mistakes like Devon's, it is essential to carefully read and understand the problem, and to simplify expressions correctly. This can be achieved by:

Breaking down complex problems into smaller, more manageable parts
Identifying and combining like terms
Eliminating unnecessary calculations
Checking the answer for accuracy

Q: What are some common mistakes to avoid when calculating surface area?

A: Some common mistakes to avoid when calculating surface area include:

Failing to simplify expressions correctly
Not combining like terms
Not eliminating unnecessary calculations
Not checking the answer for accuracy

Q: How can I practice surface area calculations?

A: To practice surface area calculations, you can try the following:

Work through examples and exercises in your textbook or online resources
Practice calculating surface area for different shapes, such as rectangles, triangles, and circles
Use online calculators or software to check your answers and identify areas for improvement

Conclusion

In conclusion, surface area calculations are an essential part of mathematics, engineering, and design. By understanding the formula for surface area and simplifying expressions correctly, you can avoid making mistakes like Devon's and arrive at the correct answer. Remember to practice regularly and seek help when needed to improve your skills in surface area calculations.