To determine the area of an equilateral triangle with sides of 2 yards and a height of 4.25 feet, follow these step-by-step instructions:
1. Convert the length of the sides from yards to feet:
Since 1 yard is equal to 3 feet, multiply the side length by 3.
[tex]\[
\text{Side length in feet} = 2 \text{ yards} \times 3 \text{ feet per yard} = 6 \text{ feet}
\][/tex]
2. Use the formula for the area of a triangle:
[tex]\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
\][/tex]
Here, the base is the side length of the triangle (which we converted to feet) and the height is given directly in feet.
3. Calculate the area:
Substitute the base and height into the formula:
[tex]\[
\text{Area} = \frac{1}{2} \times 6 \text{ feet} \times 4.25 \text{ feet}
\][/tex]
[tex]\[
\text{Area} = \frac{1}{2} \times 25.5 \text{ feet}^2
\][/tex]
[tex]\[
\text{Area} = 12.75 \text{ feet}^2
\][/tex]
Therefore, the area of the equilateral triangle is:
[tex]\[
12.75 \text{ ft}^2
\][/tex]
Thus, the correct answer is [tex]$12.75 \text{ ft}^2$[/tex].
