1. **State the problem:** We are given a kite PLAY with PA = 12 cm and LY = 6 cm. We need to find the area of kite PLAY. 2. **Recall the formula for the area of a kite:** The area of a kite is given by $$\text{Area} = \frac{1}{2} \times d_1 \times d_2$$ where $d_1$ and $d_2$ are the lengths of the diagonals. 3. **Identify the diagonals:** In kite PLAY, the diagonals are $PA$ and $LY$. 4. **Calculate the area:** Substitute the given values: $$\text{Area} = \frac{1}{2} \times 12 \times 6 = \frac{1}{2} \times 72 = 36$$ 5. **Answer:** The area of kite PLAY is $36$ cm$^2$. 6. **Theorem used:** The area formula is justified by the property that the diagonals of a kite are perpendicular and the area can be found by summing the areas of the right triangles formed, which leads to the formula $\frac{1}{2} d_1 d_2$. --- Since the user asked to solve and answer, only the first problem is solved here as per instructions.