https://file.aiquickdraw.com/mathbot/file/1727999310949645jazp2.jpg

Let's break this problem down into two parts based on the given image.

### Part a: Find the area of the banner.

The dimensions of the banner are:
- Height = \(1 \frac{1}{2}\) feet = 1.5 feet
- Length = \(4 \frac{2}{3}\) feet = \(4 + \frac{2}{3} = \frac{14}{3}\) feet

The area \(A\) of a rectangle is given by the formula:
\[
A = \text{Length} \times \text{Height}
\]

Substituting the values:
\[
A = \left(\frac{14}{3}\right) \times 1.5 = \frac{14}{3} \times \frac{3}{2} = \frac{42}{6} = 7 \text{ square feet}
\]

So, the area of the original banner is **7 square feet**.

### Part b: Find the area of the new banner with a border added.

Now, a \(\frac{1}{4}\)-foot border is added on each side. This increases both the height and length by twice the border size (since it's added on both sides).

- New Height = \(1.5 + 2 \times \frac{1}{4} = 1.5 + 0.5 = 2\) feet
- New Length = \(\frac{14}{3} + 2 \times \frac{1}{4} = \frac{14}{3} + \frac{2}{4} = \frac{14}{3} + \frac{1}{2} = \frac{28}{6} + \frac{3}{6} = \frac{31}{6}\) feet

Now, the new area \(A_{\text{new}}\) is:
\[
A_{\text{new}} = \text{New Length} \times \text{New Height}
\]
\[
A_{\text{new}} = \frac{31}{6} \times 2 = \frac{62}{6} = \frac{31}{3} \approx 10.33 \text{ square feet}
\]

So, the area of the new banner is approximately **10.33 square feet**.

---

Would you like more details on any part of this solution, or do you have any questions?

### Here are some related questions:
1. What is the perimeter of the original banner?
2. What would be the total perimeter of the new banner with the border?
3. How would the area change if the border added was 1 foot instead of \(\frac{1}{4}\) foot?
4. What is the fractional difference in area between the original banner and the new banner?
5. If the banner's height increased by 50%, what would be the new area?

### Tip:
Always add the border length on both sides when adjusting dimensions for area calculations involving frames or borders.

You make a banner for a football rally. (a) What is the area of the banner? (b) You add a 1/4-foot border on each side. What is the area of the new banner?

Learn how to calculate the area of a football rally banner with and without a 1/4-foot border. This problem covers geometry concepts, including the area of rectangles and working with fractions. Ideal for students in Grades 5-7.

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