Sure, I'd be happy to help you find the area of a parallelogram given the base and the altitude. Here’s a step-by-step solution:
### Given:
- Base = [tex]\( x \)[/tex] yards
- Altitude = [tex]\( 3y \)[/tex] feet
### Note on Units:
The base is given in yards and the altitude is given in feet. To calculate the area, the base and the altitude must be in the same unit. Thus, we need to convert either the base to feet or the altitude to yards.
Since 1 yard = 3 feet, we can convert the altitude from feet to yards:
[tex]\[
\text{Altitude in yards} = \frac{3y \text{ feet}}{3} = y \text{ yards}
\][/tex]
### Formula for the Area of a Parallelogram:
The area [tex]\( A \)[/tex] of a parallelogram is given by the formula:
[tex]\[
A = \text{base} \times \text{altitude}
\][/tex]
Substituting the values we have:
[tex]\[
A = x \text{ (yards)} \times y \text{ (yards)} = xy \text{ (square yards)}
\][/tex]
### Answer Choices:
1. [tex]\( 9xy \)[/tex] sq. ft.
2. [tex]\( 3xy \)[/tex] sq. ft.
3. [tex]\( \frac{1}{3}xy \)[/tex] sq. ft.
To equate to these choices, notice that these areas are given in square feet. Let's convert our area in square yards to square feet.
[tex]\[
1 \text{ (square yard)} = 3^2 \text{ (square feet)} = 9 \text{ (square feet)}
\][/tex]
Thus,
[tex]\[
xy \text{ (square yards)} = xy \times 9 \text{ (square feet)} = 9xy \text{ (square feet)}
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{9xy \text{ sq. ft.}}
\][/tex]
