Let's analyze the problem based on the provided image and information.

Problem Breakdown:

• The pool's dimensions are given as a mix of known and unknown side lengths.
• You are told that the side labeled x is 5 times the shortest side adjacent to it. From the diagram, the shortest adjacent side is 4 feet.
• Therefore, the length of side x is: $x = 5 \times 4 = 20 \, \text{feet}$

Now, let's find the total area of the pool. The pool can be divided into two rectangular sections:

1. The larger rectangle with dimensions 20 feet (side x) and 16 feet.
2. The smaller rectangle with dimensions 8 feet and 12 feet.

Step 1: Calculate the area of the larger rectangle

The area of a rectangle is given by: $\text{Area} = \text{length} \times \text{width}$ For the larger rectangle: $\text{Area}_{\text{large}} = 20 \times 16 = 320 \, \text{square feet}$

Step 2: Calculate the area of the smaller rectangle

For the smaller rectangle: $\text{Area}_{\text{small}} = 12 \times 8 = 96 \, \text{square feet}$

Step 3: Add both areas

The total area of the pool is: $\text{Total Area} = 320 + 96 = 416 \, \text{square feet}$

Final Answer:

The area of the pool is 416 square feet.

Would you like further details or have any questions about this solution? Here are some follow-up questions that you might find useful:

1. How do you calculate the area of irregular shapes made up of rectangles?
2. What other ways can we divide complex shapes to simplify area calculations?
3. How would the problem change if the dimensions of the smaller rectangle were different?
4. How does the relationship between the sides (e.g., 5 times the shortest side) help solve the problem?
5. Can you use this method to calculate volumes, such as the volume of a swimming pool?

Tip: Always check if a shape can be decomposed into simpler components, like rectangles or triangles, to make calculations easier.