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### Part (a): Finding the area that needs stucco

We need to calculate the surface area of the warehouse walls that require stucco, excluding the roof, windows, and doors.

The warehouse has:
- Front and back walls each measuring 24 ft by 15 ft.
- Side walls each measuring 30 ft by 15 ft.

The front has:
- A rollup door of size 16 ft by 9 ft.
- An entry door of size 3 ft by 7 ft.
- A window of size 162 in by 32 in (convert this to feet: 162 in = 13.5 ft, and 32 in = 2.67 ft).

#### Step 1: Calculate the area of the front and back walls
- Area of each wall = height × width = 15 ft × 24 ft = 360 ft².
- For two walls, the total area = 2 × 360 = 720 ft².

Now subtract the area of the doors and window from the front wall:
- Rollup door area = 16 ft × 9 ft = 144 ft².
- Entry door area = 3 ft × 7 ft = 21 ft².
- Window area = 13.5 ft × 2.67 ft ≈ 36.045 ft².

So, total front wall area after subtracting:
\[
360 - (144 + 21 + 36.045) = 360 - 201.045 = 158.955 \, \text{ft}² \text{(for the front wall)}.
\]

The back wall has no windows or doors, so it remains 360 ft².

#### Step 2: Calculate the area of the side walls
- Each side wall area = height × width = 15 ft × 30 ft = 450 ft².
- For two side walls, the total area = 2 × 450 = 900 ft².

#### Step 3: Total surface area requiring stucco
The total area that requires stucco is:
\[
158.955 \, (\text{front wall}) + 360 \, (\text{back wall}) + 900 \, (\text{side walls}) = 1418.955 \, \text{ft}².
\]

Rounding to the nearest whole number, the area that needs stucco is:
\[
\boxed{1419 \, \text{ft}²}.
\]

### Part (b): Number of stucco bags required

Each bag covers 110 ft². So, the number of bags required is:
\[
\frac{1419 \, \text{ft}²}{110 \, \text{ft}²/\text{bag}} = 12.9.
\]
Since partial bags can't be bought, you'll need 13 bags. So, the answer is:
\[
\boxed{13 \, \text{bags}}.
\]

### Part (c): Total cost of stucco

If each bag costs $13.50, the total cost is:
\[
13 \, \text{bags} \times 13.50 \, \text{\$} = 175.50 \, \text{\$}.
\]
Thus, the total cost is:
\[
\boxed{175.50 \, \text{\$}}.
\]

Let me know if you'd like further clarification or more details! Here are 5 follow-up questions:

1. How would the calculations change if the warehouse height were increased by 5 feet?
2. If the window were on the side wall, how would that impact the stucco area?
3. How much would the cost increase if the price of stucco per bag rose by 20%?
4. What is the total surface area of all the walls, including the doors and windows?
5. How many bags would be needed if each bag covered only 90 ft² instead of 110 ft²?

**Tip:** When calculating surface areas with windows or doors, always subtract these areas from the total wall area to avoid overestimating materials needed.

A warehouse, whose dimensions are shown below, needs stucco. The front and back of the warehouse each have a rollup door measuring 16 ft by 9 ft. The side of the warehouse facing the parking lot has a window measuring 162 in by 32 in and an entry door measuring 3 ft by 7 ft. The other side of the warehouse has no window or door. Use the given information to answer the questions.

Solve a warehouse stucco problem by calculating the surface area excluding doors and windows. Learn how to use area formulas, subtracting areas for openings. Suitable for students in Grades 9-12.

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