Calculating the Area of the Pennant

Oct 13, 2025 by vinooalluri.com 32 views

Introduction

As the spirit week approaches, Tameeka is tasked with designing a school pennant that will showcase the school's spirit and pride. The pennant's design requires careful consideration of its dimensions and the amount of paper needed to create it. In this article, we will explore the math behind designing a school pennant and determine if Tameeka has enough paper to complete her project.

Understanding the Problem

Tameeka wants the base of the pennant to be $3 \frac{1}{2}$ feet and the height to be $6 \frac{1}{2}$ feet. To determine if she has enough paper, we need to calculate the area of the pennant. The area of a rectangle, such as the pennant, is calculated by multiplying the length (base) by the width (height).

Calculating the Area of the Pennant

To calculate the area of the pennant, we need to multiply the base by the height.

Area = base \times height

In this case, the base is $3 \frac{1}{2}$ feet and the height is $6 \frac{1}{2}$ feet. We can convert the mixed numbers to improper fractions to make the calculation easier.

3 \frac{1}{2} = \frac{7}{2}
6 \frac{1}{2} = \frac{13}{2}

Now, we can multiply the base and height to find the area.

Area = \frac{7}{2} \times \frac{13}{2}
= \frac{91}{4}
= 22.75

Determining if Tameeka Has Enough Paper

Tameeka has 20 square feet of paper available. To determine if she has enough paper, we need to compare the calculated area of the pennant to the amount of paper she has.

Area of pennant = 22.75 square feet
Paper available = 20 square feet

Since the area of the pennant (22.75 square feet) is greater than the amount of paper available (20 square feet), Tameeka does not have enough paper to complete her project.

Conclusion

In conclusion, Tameeka's school pennant design requires a base of $3 \frac{1}{2}$ feet and a height of $6 \frac{1}{2}$ feet. To determine if she has enough paper, we calculated the area of the pennant and compared it to the amount of paper available. Unfortunately, Tameeka does not have enough paper to complete her project. However, she can consider using a different design or adjusting the dimensions of the pennant to use the available paper more efficiently.

Tips for Designing a School Pennant

When designing a school pennant, consider the following tips:

Keep it simple: A simple design is easier to create and requires less paper.
Use a smaller base: A smaller base will require less paper and make the pennant easier to handle.
Adjust the height: Adjusting the height of the pennant can also help reduce the amount of paper needed.
Use a different shape: Consider using a different shape, such as a triangle or a circle, which may require less paper than a rectangle.

Q&A: Designing a School Pennant

Q: What is the formula for calculating the area of a rectangle?

A: The formula for calculating the area of a rectangle is:

Area = base \times height

Q: How do I convert a mixed number to an improper fraction?

A: To convert a mixed number to an improper fraction, follow these steps:

Multiply the whole number part by the denominator.
Add the product to the numerator.
Write the result as an improper fraction.

For example, to convert $3 \frac{1}{2}$ to an improper fraction:

Multiply 3 by 2: 3 \times 2 = 6
Add 6 to 1: 6 + 1 = 7
Write the result as an improper fraction: $\frac{7}{2}$

Q: How do I calculate the area of a pennant with a base of $3 \frac{1}{2}$ feet and a height of $6 \frac{1}{2}$ feet?

A: To calculate the area of the pennant, follow these steps:

Convert the mixed numbers to improper fractions: $3 \frac{1}{2} = \frac{7}{2}$ and $6 \frac{1}{2} = \frac{13}{2}$
Multiply the base and height: $\frac{7}{2} \times \frac{13}{2} = \frac{91}{4}$
Simplify the fraction: $\frac{91}{4} = 22.75$

Q: How do I determine if I have enough paper to create a pennant?

A: To determine if you have enough paper, compare the calculated area of the pennant to the amount of paper available. If the area of the pennant is greater than the amount of paper available, you do not have enough paper.

Q: What are some tips for designing a school pennant?

A: Here are some tips for designing a school pennant:

Keep it simple: A simple design is easier to create and requires less paper.
Use a smaller base: A smaller base will require less paper and make the pennant easier to handle.
Adjust the height: Adjusting the height of the pennant can also help reduce the amount of paper needed.
Use a different shape: Consider using a different shape, such as a triangle or a circle, which may require less paper than a rectangle.

Q: What are some common mistakes to avoid when designing a school pennant?

A: Here are some common mistakes to avoid when designing a school pennant:

Not considering the amount of paper available: Make sure to calculate the area of the pennant and compare it to the amount of paper available before starting the project.
Not using a scale: Using a scale can help you create a more accurate design and avoid wasting paper.
Not considering the size of the pennant: Make sure the pennant is the right size for the school's spirit week or other events.

By following these tips and avoiding common mistakes, you can create a beautiful school pennant that showcases the school's spirit and pride while using the available paper efficiently.