1. **State the problem:** We need to find the perimeter of an equilateral triangle where each side length is $2 \frac{1}{4}$ kilometers. 2. **Recall the formula for the perimeter of a triangle:** $$\text{Perimeter} = \text{sum of all side lengths}$$ Since the triangle is equilateral, all sides are equal, so: $$\text{Perimeter} = 3 \times \text{side length}$$ 3. **Convert the mixed number to an improper fraction:** $$2 \frac{1}{4} = \frac{2 \times 4 + 1}{4} = \frac{9}{4}$$ 4. **Calculate the perimeter:** $$\text{Perimeter} = 3 \times \frac{9}{4} = \frac{27}{4}$$ 5. **Convert the improper fraction to a mixed number:** $$\frac{27}{4} = 6 \frac{3}{4}$$ 6. **Final answer:** The perimeter of the triangle is $6 \frac{3}{4}$ kilometers or $\frac{27}{4}$ kilometers.