1c. Simplify and state the value of the variable that makes the expression zero. (y2-7y+12)/(y-9)

The shaded region consists of two parts: a rectangle on the left and a trapezoid on the right.

• The rectangle has a width of $2.5 \text{ m}$ and a height of $3 \text{ m}$.
• The trapezoid has a height of $3 \text{ m}$. Its top base is $2.5 \text{ m}$. Its bottom base is the total bottom length minus the rectangle's width: $10.5 \text{ m} - 2.5 \text{ m} = 8 \text{ m}$.

The area of the rectangle $A_R$ is given by:

$$A_R = \text{width} \times \text{height}$$

The area of the trapezoid $A_T$ is given by:

$$A_T = \frac{1}{2} \times (\text{top base} + \text{bottom base}) \times \text{height}$$

The total shaded area $A$ is the sum of these two areas:

$$A = A_R + A_T$$

Substitute the dimensions into the area formulas:

$$A = (2.5 \text{ m} \times 3 \text{ m}) + \left(\frac{1}{2} \times (2.5 \text{ m} + 8 \text{ m}) \times 3 \text{ m}\right)$$

Notice that the height, $3 \text{ m}$, is a common factor in both terms. We can factor it out using the distributive property:

$$A = 3 \text{ m} \times \left(2.5 \text{ m} + \frac{1}{2} \times (2.5 \text{ m} + 8 \text{ m})\right)$$ $$A = 3 \text{ m} \times \left(2.5 \text{ m} + \frac{1}{2} \times (10.5 \text{ m})\right)$$ $$A = 3 \text{ m} \times (2.5 \text{ m} + 5.25 \text{ m})$$ $$A = 3 \text{ m} \times (7.75 \text{ m})$$

$$A = 23.25 \text{ m}^2$$

The area of the shaded portion is $\text{23.25 m}^2$.