1. **Stating the problem:** We are given a rectangle with dimensions $(2x - 2)$ ft by $(-x + 2)$ ft and an algebra tiles grid representing the product of these binomials. 2. **Formula used:** The area of a rectangle is given by the product of its length and width: $$\text{Area} = \text{length} \times \text{width}$$ Here, the length is $(2x - 2)$ and the width is $(-x + 2)$. 3. **Multiplying the binomials:** $$ (2x - 2)(-x + 2) $$ Use the distributive property (FOIL method): $$ = 2x \times (-x) + 2x \times 2 - 2 \times (-x) - 2 \times 2 $$ $$ = -2x^2 + 4x + 2x - 4 $$ 4. **Combine like terms:** $$ -2x^2 + (4x + 2x) - 4 = -2x^2 + 6x - 4 $$ 5. **Interpretation of algebra tiles:** - The tiles represent each term: $x^2$ tiles (red outlined for negative), $x$ tiles (green outlined for positive), and unit tiles (1) with appropriate signs. - The red outlines indicate negative terms, matching the $-2x^2$ and $-4$ in the expression. 6. **Final answer:** The area of the rectangle is $$\boxed{-2x^2 + 6x - 4}$$ This matches the algebra tiles representation and the product of the binomials.