1. **State the problem:** Find the area of the triangle with vertices at points (0, 0), (6, 0), and (3, 8). 2. **Formula used:** The area of a triangle given coordinates $(x_1, y_1)$, $(x_2, y_2)$, and $(x_3, y_3)$ is $$\text{Area} = \frac{1}{2} \left| x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2) \right|$$ 3. **Apply the formula:** Substitute the points: $$x_1=0, y_1=0; \quad x_2=6, y_2=0; \quad x_3=3, y_3=8$$ Calculate inside the absolute value: $$0(0 - 8) + 6(8 - 0) + 3(0 - 0) = 0 + 48 + 0 = 48$$ 4. **Calculate the area:** $$\text{Area} = \frac{1}{2} |48| = \frac{1}{2} \times 48 = 24$$ 5. **Interpretation:** The area of the triangle is 24 square units.