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!

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.