1. The problem asks for the area of a triangle with a base of $3 \frac{2}{3}$ yards and a height of $2 \frac{1}{4}$ yards. 2. The formula for the area of a triangle is: $$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$$ 3. Convert the mixed numbers to improper fractions: $$3 \frac{2}{3} = \frac{11}{3}$$ $$2 \frac{1}{4} = \frac{9}{4}$$ 4. Substitute the values into the formula: $$\text{Area} = \frac{1}{2} \times \frac{11}{3} \times \frac{9}{4}$$ 5. Multiply the numerators and denominators: $$\text{Area} = \frac{1 \times 11 \times 9}{2 \times 3 \times 4} = \frac{99}{24}$$ 6. Simplify the fraction by dividing numerator and denominator by their greatest common divisor, which is 3: $$\text{Area} = \frac{\cancel{99}^ {33}}{\cancel{24}^{8}} = \frac{33}{8}$$ 7. Convert the improper fraction to a mixed number: $$\frac{33}{8} = 4 \frac{1}{8}$$ 8. Therefore, the area of the triangle is $4 \frac{1}{8}$ square yards.