https://file.aiquickdraw.com/mathbot/file/172643781386919ud74wo.jpg

Let's break down and solve the two parts of the problem.

### Problem 3a:
The map of the park has dimensions of 4 inches by 6 inches, and the scale is \( 1 \text{ inch} = 30 \text{ miles} \).

1. **Length of the park**:
   - In the real world, the length is \( 4 \text{ inches} \times 30 \text{ miles/inch} = 120 \text{ miles} \).

2. **Width of the park**:
   - In the real world, the width is \( 6 \text{ inches} \times 30 \text{ miles/inch} = 180 \text{ miles} \).

Now, to find the actual area:
- The area is \( \text{Length} \times \text{Width} \).
- \( \text{Area} = 120 \text{ miles} \times 180 \text{ miles} = 21,600 \text{ square miles} \).

### Problem 3b:
The map needs to fit in a brochure with an area of 6 square inches. We need to find a new scale.

- The current area of the map on paper is \( 4 \times 6 = 24 \text{ square inches} \).
- The scale factor is given by the ratio of the new area to the old area:  
  \[
  \text{Scale factor} = \sqrt{\frac{\text{New area}}{\text{Old area}}} = \sqrt{\frac{6}{24}} = \frac{1}{2}.
  \]

Thus, the new scale should be half the current scale. Since the current scale is \( 1 \text{ inch} = 30 \text{ miles} \), the new scale will be:
\[
1 \text{ inch} = 60 \text{ miles}.
\]

Let me know if you'd like further clarification or details!

Here are 5 related questions to deepen your understanding:
1. How would the area change if the scale were 1 inch = 15 miles?
2. If the brochure only allowed 3 square inches, what would the new scale be?
3. What if the map dimensions were 5 inches by 7 inches with the same scale of 1 inch = 30 miles?
4. How does changing the map's scale affect the perception of distance?
5. Can you calculate the perimeter of the park at the given scale?

**Tip:** Always double-check your units when working with different scales in maps to avoid confusion!

A map of a rectangular park has a length of 4 inches and a width of 6 inches. It uses a scale of 1 inch for every 30 miles. What is the actual area of the park? The map also needs to be reproduced at a different scale so that it has an area of 6 square inches. At what scale should the map be reproduced to fit in a brochure?

Solve a problem involving the area of a rectangular park where the map has a scale of 1 inch = 30 miles. The park's actual area and a new scale factor to fit the map in a brochure are calculated. Learn about area calculation, scale factors, and the impact on map reproduction. Suitable for Grades 7-10.

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