https://file.aiquickdraw.com/mathbot/file/173008150022674yzltbm.jpg

Let's go through each of the conversions:

### Conversion Factors:
1. **Square Feet to Square Yards**: \(1 \, \text{yd}^2 = 9 \, \text{ft}^2\)
2. **Square Yards to Square Feet**: \(1 \, \text{yd}^2 = 9 \, \text{ft}^2\) (inverse of the above)
3. **Square Miles to Acres**: \(1 \, \text{mi}^2 = 640 \, \text{acres}\)
4. **Acres to Square Yards**: \(1 \, \text{acre} = 4,840 \, \text{yd}^2\)

### Solutions:

**a. \(81 \, \text{ft}^2 = \, ? \, \text{yd}^2\)**  
To convert square feet to square yards, divide by 9:
\[
\frac{81 \, \text{ft}^2}{9} = 9 \, \text{yd}^2
\]
**Answer:** \(9 \, \text{yd}^2\)

**b. \(10^5 \, \text{yd}^2 = \, ? \, \text{ft}^2\)**  
To convert square yards to square feet, multiply by 9:
\[
10^5 \, \text{yd}^2 \times 9 = 900,000 \, \text{ft}^2
\]
**Answer:** \(900,000 \, \text{ft}^2\)

**c. \(6.5 \, \text{mi}^2 = \, ? \, \text{acres}\)**  
To convert square miles to acres, multiply by 640:
\[
6.5 \, \text{mi}^2 \times 640 = 4160 \, \text{acres}
\]
**Answer:** \(4160 \, \text{acres}\)

**d. \(3 \, \text{acres} = \, ? \, \text{yd}^2\)**  
To convert acres to square yards, multiply by 4840:
\[
3 \, \text{acres} \times 4840 = 14,520 \, \text{yd}^2
\]
**Answer:** \(14,520 \, \text{yd}^2\)

Let me know if you need more details or have any questions!

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### Related Questions
1. How do you convert between square meters and square feet?
2. What is the conversion factor for acres to square miles?
3. How can you convert square centimeters to square meters?
4. How do you convert hectares to square kilometers?
5. What is the area of 2.5 square miles in square yards?

### Tip
Always double-check conversion factors, as some units (like acres and hectares) can be tricky to remember.

Complete the following conversions:
a. 81 ft² = _______ yd²
b. 10^5 yd² = _______ ft²
c. 6.5 mi² = _______ acres
d. 3 acres = _______ yd²

Solve area unit conversion problems involving square feet, square yards, square miles, and acres. This example includes conversions for 81 ft² to yd², 10^5 yd² to ft², 6.5 mi² to acres, and 3 acres to yd², providing a step-by-step solution suitable for Grades 6-8.

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