https://file.aiquickdraw.com/mathbot/file/1728000473625fvqmhbxd.jpg

Let's work through each part of the problem based on the information visible in the image.

### a. Number of squares Kelly needs to make:
The quilt is a rectangle with dimensions 7 feet 4 inches by 6 feet 5 inches. We can first convert both dimensions into inches:

- 7 feet 4 inches = \( 7 \times 12 + 4 = 84 + 4 = 88 \) inches.
- 6 feet 5 inches = \( 6 \times 12 + 5 = 72 + 5 = 77 \) inches.

Now, we divide these dimensions by the side length of each square (11 inches per side):
\[
\frac{88}{11} = 8 \quad \text{and} \quad \frac{77}{11} = 7
\]

So, the total number of squares is:
\[
8 \times 7 = 56 \text{ squares.}
\]

### b. Area of each square before the circle is sewn:
Each square has a side length of 11 inches, so the area of one square is:
\[
11^2 = 121 \text{ square inches.}
\]

### c. Area of each circle:
The circle has a diameter of 6 inches, so the radius is half of that:
\[
r = \frac{6}{2} = 3 \text{ inches.}
\]
The area of each circle is:
\[
A = \pi r^2 = \pi \times 3^2 = 9\pi \approx 28.3 \text{ square inches.}
\]

### d. Total area of all the circles:
There are 56 squares, and each square contains a circle, so the total area of all the circles is:
\[
56 \times 28.3 \approx 1584.8 \text{ square inches.}
\]

### e. Length of the border around the entire quilt:
The perimeter of the quilt is the sum of all four sides. The dimensions of the quilt are 88 inches by 77 inches, so the perimeter is:
\[
2 \times (88 + 77) = 2 \times 165 = 330 \text{ inches.}
\]

Let me know if you'd like further clarification or details on any part of this solution!

---

Here are five related questions for further practice:
1. How would the number of squares change if each square were 12 inches on a side?
2. What would the total area of all the squares be if the quilt dimensions were 8 feet by 5 feet?
3. How would the area of each circle change if the diameter were 8 inches instead of 6 inches?
4. If Kelly made a second quilt with different dimensions, how would she calculate the number of squares needed?
5. How would the total length of the border change if the quilt dimensions were increased by 1 foot on each side?

**Tip:** Always convert measurements to the same units (like inches) before performing calculations for consistency.

Kelly decides that the quilt will be a rectangle 7 feet 4 inches by 6 feet 5 inches. How many squares will she need to make for the quilt? What is the area of each square, and what is the total area of the circles sewn on the quilt? What is the total length of the border around the quilt?

Solve a geometry problem related to designing a quilt by calculating the number of squares needed, the areas of squares and circles, and the total border length. This problem involves unit conversions, area formulas, and perimeter calculations, suitable for Grades 6-8.

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