1. **State the problem:** Find the area of the kite with diagonals of lengths 1 and 2. 2. **Formula for the area of a kite:** The area $A$ of a kite is given by $$A = \frac{1}{2} \times d_1 \times d_2$$ where $d_1$ and $d_2$ are the lengths of the diagonals. 3. **Apply the formula:** Here, $d_1 = 1$ and $d_2 = 2$. 4. **Calculate the area:** $$A = \frac{1}{2} \times 1 \times 2$$ 5. **Simplify:** $$A = \frac{1}{2} \times 2 = \cancel{\frac{1}{2}} \times \cancel{2} = 1$$ 6. **Conclusion:** The area of the kite is 1 square unit.