1. **Problem Statement:** Find the area of the irregular shape with a rectangular cut-out on the top-left side, given side lengths labeled as $x+5$, $3$, $x-2$, and $x$. 2. **Understanding the shape:** The figure can be seen as a large rectangle minus a smaller rectangle cut out from the top-left corner. 3. **Formula for area of a rectangle:** $$\text{Area} = \text{length} \times \text{width}$$ 4. **Calculate the area of the large rectangle:** - The large rectangle has width $x+5$ and height $x$. - So, its area is: $$A_{large} = (x+5) \times x = x(x+5) = x^2 + 5x$$ 5. **Calculate the area of the cut-out rectangle:** - The cut-out has width $3$ and height $x-2$. - So, its area is: $$A_{cut} = 3 \times (x-2) = 3x - 6$$ 6. **Calculate the area of the shaded shape:** - Subtract the cut-out area from the large rectangle area: $$A = A_{large} - A_{cut} = (x^2 + 5x) - (3x - 6)$$ - Simplify: $$A = x^2 + 5x - 3x + 6 = x^2 + 2x + 6$$ 7. **Final answer:** $$\boxed{A = x^2 + 2x + 6}$$ This expression gives the area of the shaded shape in expanded form in terms of $x$.