1. **State the problem:** We need to find the area of a square given its vertices at approximately (1.5, 3), (2, 6), (5, 5), and (4, 2.5). 2. **Recall the formula for the area of a square:** $$\text{Area} = \text{side}^2$$ 3. **Find the length of one side:** Since the figure is a square, all sides are equal. We calculate the distance between two adjacent vertices using the distance formula: $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ 4. **Calculate the distance between points (1.5, 3) and (2, 6):** $$d = \sqrt{(2 - 1.5)^2 + (6 - 3)^2} = \sqrt{0.5^2 + 3^2} = \sqrt{0.25 + 9} = \sqrt{9.25}$$ 5. **Simplify the distance:** $$d = \sqrt{9.25} \approx 3.041381265$$ 6. **Calculate the area:** $$\text{Area} = d^2 = (3.041381265)^2 = 9.25$$ 7. **Round to the tenths place:** $$9.25 \approx 9.3$$ **Final answer:** The area of the square is approximately **9.3** square units.