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To solve each of these conversion problems, let’s use the following key conversions:

1. **Square Feet to Square Yards**: \(1 \, \text{yd}^2 = 9 \, \text{ft}^2\)
2. **Square Yards to Square Feet**: \(1 \, \text{yd}^2 = 9 \, \text{ft}^2\), so to convert back, multiply by 9.
3. **Square Miles to Acres**: \(1 \, \text{mi}^2 = 640 \, \text{acres}\)
4. **Acres to Square Yards**: \(1 \, \text{acre} = 4840 \, \text{yd}^2\)

Now, let’s go through each part:

### Part (a)
Convert \(117 \, \text{ft}^2\) to \(\text{yd}^2\).

\[
117 \, \text{ft}^2 \times \frac{1 \, \text{yd}^2}{9 \, \text{ft}^2} = \frac{117}{9} = 13 \, \text{yd}^2
\]

So, \(117 \, \text{ft}^2 = 13 \, \text{yd}^2\).

### Part (b)
Convert \(10^6 \, \text{yd}^2\) to \(\text{ft}^2\).

\[
10^6 \, \text{yd}^2 \times 9 \, \text{ft}^2 = 9 \times 10^6 \, \text{ft}^2 = 9{,}000{,}000 \, \text{ft}^2
\]

So, \(10^6 \, \text{yd}^2 = 9{,}000{,}000 \, \text{ft}^2\).

### Part (c)
Convert \(5.5 \, \text{mi}^2\) to acres.

\[
5.5 \, \text{mi}^2 \times 640 \, \text{acres} = 3520 \, \text{acres}
\]

So, \(5.5 \, \text{mi}^2 = 3520 \, \text{acres}\).

### Part (d)
Convert \(4 \, \text{acres}\) to \(\text{yd}^2\).

\[
4 \, \text{acres} \times 4840 \, \text{yd}^2 = 19360 \, \text{yd}^2
\]

So, \(4 \, \text{acres} = 19360 \, \text{yd}^2\).

### Summary of Answers:
- **(a)** \(117 \, \text{ft}^2 = 13 \, \text{yd}^2\)
- **(b)** \(10^6 \, \text{yd}^2 = 9{,}000{,}000 \, \text{ft}^2\)
- **(c)** \(5.5 \, \text{mi}^2 = 3520 \, \text{acres}\)
- **(d)** \(4 \, \text{acres} = 19360 \, \text{yd}^2\)

Would you like further explanation on any of these conversions?

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Here are some related questions:
1. How do you convert square yards to square feet?
2. What is the process for converting square miles to acres?
3. Why does 1 acre equal 4840 square yards?
4. Can you convert directly from square feet to acres?
5. How can area conversions be applied in real-world contexts?

**Tip:** Remember to check the units carefully in area conversions since they're squared, which often requires multiplying or dividing by conversion factors squared as well.

Complete the following conversions:

a. 117 ft² = ______ yd²
b. 10^6 yd² = ______ ft²
c. 5.5 mi² = ______ acres
d. 4 acres = ______ yd²

Learn how to solve unit conversion problems involving area measurements. Convert square feet to square yards, square yards to square feet, square miles to acres, and acres to square yards. Suitable for students in Grades 8-10.

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