Why Expression B is Correct

Oct 13, 2025 by talynt.org 86 views

When it comes to finding the area of a poster with multiple colored sections, it's essential to break down the problem into manageable parts. In this article, we'll explore the different expressions for the area of a poster and determine which one is written as the sum of the areas of each colored section.

The Poster's Dimensions

Let's assume the poster has a rectangular shape with a length of 3 units and a width of a units. The colored sections are divided into two parts: a larger section with an area of 3a square units and a smaller section with an area of a + 1/2 square units.

Expression A: $\left(a+\frac{1}{2}\right)(3+1$ ]

Expression A is given as $\left(a+\frac{1}{2}\right)(3+1$ ]. However, this expression is incomplete and doesn't accurately represent the area of the poster. To find the correct expression, we need to multiply the width of the smaller section by the length of the entire poster.

Expression B: $3\left(a+\frac{1}{2}\right)+\left(a+\frac{1}{2}\right$ ]

Expression B is given as $3\left(a+\frac{1}{2}\right)+\left(a+\frac{1}{2}\right$ ]. This expression represents the area of the entire poster as the sum of the areas of each colored section. The first term, $3\left(a+\frac{1}{2}\right)$ , represents the area of the larger section, while the second term, $\left(a+\frac{1}{2}\right)$ , represents the area of the smaller section.

Expression C: $4a+2$

Expression C is given as $4a+2$ . This expression represents the area of the entire poster, but it doesn't accurately reflect the sum of the areas of each colored section.

Conclusion

Based on the analysis above, the correct expression for the area of the poster is written as the sum of the areas of each colored section is Expression B: $3\left(a+\frac{1}{2}\right)+\left(a+\frac{1}{2}\right$ ].

Why Expression B is Correct

Expression B is correct because it accurately represents the area of the entire poster as the sum of the areas of each colored section. The first term, $3\left(a+\frac{1}{2}\right)$ , represents the area of the larger section, while the second term, $\left(a+\frac{1}{2}\right)$ , represents the area of the smaller section.

Tips for Finding the Correct Expression

When finding the correct expression for the area of a poster, make sure to:

Break down the problem into manageable parts
Identify the dimensions of each colored section
Multiply the width of each section by the length of the entire poster
Add the areas of each section to find the total area

By following these tips, you'll be able to find the correct expression for the area of a poster and accurately represent the sum of the areas of each colored section.

Real-World Applications

Understanding how to find the area of a poster with multiple colored sections has real-world applications in various fields, such as:

Graphic design: When designing a poster, it's essential to consider the dimensions of each colored section and calculate the total area to ensure accurate printing.
Architecture: When designing a building, architects need to consider the dimensions of each section and calculate the total area to ensure accurate construction.
Engineering: When designing a system, engineers need to consider the dimensions of each component and calculate the total area to ensure accurate functionality.

By understanding how to find the area of a poster with multiple colored sections, you'll be able to apply this knowledge in various real-world scenarios and make informed decisions.

Conclusion

In our previous article, we explored the different expressions for the area of a poster and determined which one is written as the sum of the areas of each colored section. In this article, we'll answer some frequently asked questions related to finding the area of a colored poster.

Q: What is the formula for finding the area of a colored poster?

A: The formula for finding the area of a colored poster is:

Area = Length x Width

However, when dealing with a colored poster, we need to consider the dimensions of each colored section and calculate the total area.

Q: How do I find the area of a colored poster with multiple sections?

A: To find the area of a colored poster with multiple sections, follow these steps:

Identify the dimensions of each colored section.
Multiply the width of each section by the length of the entire poster.
Add the areas of each section to find the total area.

Q: What is the difference between Expression A and Expression B?

A: Expression A is incomplete and doesn't accurately represent the area of the poster. Expression B, on the other hand, represents the area of the entire poster as the sum of the areas of each colored section.

Q: Why is Expression B the correct expression for the area of the poster?

A: Expression B is the correct expression because it accurately represents the area of the entire poster as the sum of the areas of each colored section. The first term, $3\left(a+\frac{1}{2}\right)$ , represents the area of the larger section, while the second term, $\left(a+\frac{1}{2}\right)$ , represents the area of the smaller section.

Q: What are some real-world applications of finding the area of a colored poster?

A: Understanding how to find the area of a colored poster has real-world applications in various fields, such as:

Graphic design: When designing a poster, it's essential to consider the dimensions of each colored section and calculate the total area to ensure accurate printing.
Architecture: When designing a building, architects need to consider the dimensions of each section and calculate the total area to ensure accurate construction.
Engineering: When designing a system, engineers need to consider the dimensions of each component and calculate the total area to ensure accurate functionality.

Q: How can I apply the knowledge of finding the area of a colored poster in my daily life?

A: You can apply the knowledge of finding the area of a colored poster in your daily life by:

Using it to design posters, flyers, or brochures for work or school projects.
Calculating the area of a room or a piece of furniture to determine the amount of paint or fabric needed.
Understanding the dimensions of a building or a system to ensure accurate construction or functionality.

Q: What are some common mistakes to avoid when finding the area of a colored poster?

A: Some common mistakes to avoid when finding the area of a colored poster include:

Not considering the dimensions of each colored section.
Not multiplying the width of each section by the length of the entire poster.
Not adding the areas of each section to find the total area.

By avoiding these common mistakes, you'll be able to accurately find the area of a colored poster and apply this knowledge in various real-world scenarios.

Conclusion

In conclusion, finding the area of a colored poster is a crucial skill that has real-world applications in various fields. By understanding the formula for finding the area of a colored poster and avoiding common mistakes, you'll be able to accurately calculate the total area and apply this knowledge in your daily life.