1. **Stating the problem:** Given points A(2,2), B(4,0), and C(-2,0), find the area of triangle ABC. 2. **Formula used:** The area of a triangle with vertices at coordinates $(x_1,y_1)$, $(x_2,y_2)$, and $(x_3,y_3)$ is given by: $$\text{Area} = \frac{1}{2} \left| x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2) \right|$$ 3. **Substitute the points:** $$x_1=2, y_1=2; \quad x_2=4, y_2=0; \quad x_3=-2, y_3=0$$ 4. **Calculate the expression inside the absolute value:** $$2(0 - 0) + 4(0 - 2) + (-2)(2 - 0) = 2 \times 0 + 4 \times (-2) + (-2) \times 2 = 0 - 8 - 4 = -12$$ 5. **Calculate the area:** $$\text{Area} = \frac{1}{2} | -12 | = \frac{1}{2} \times 12 = 6$$ 6. **Interpretation:** The area of triangle ABC is 6 square units.