Let's break down the problem step by step to solve the expression for the relationship between the areas of two figures, represented in different units.

Information Provided:

• Figure 1: In meters

  • Width: 30 meters
  • Length: 40 meters
  • Area: $30 \times 40 = 1200 \, \text{m}^2$

• Figure 2: In centimeters

  • Width: 6 cm
  • Length: 8 cm
  • Area: $6 \times 8 = 48 \, \text{cm}^2$

Step 1: Relationship Between 1 cm² and Square Meters

You are given that the figures are scaled, and the scale factor is $1 \, \text{cm} = 5 \, \text{m}$. This means that for each 1 cm in the smaller figure, it represents 5 meters in the real-world figure.

So, in terms of area: $1 \, \text{cm}^2 = (5 \, \text{m})^2 = 25 \, \text{m}^2$ This tells us that each square centimeter on the smaller figure represents 25 square meters on the larger figure.

Step 2: Complete the Expression

The relationship between the areas is: $48 \, \text{cm}^2 \times 25 \, \text{m}^2/\text{cm}^2 = 1200 \, \text{m}^2$

Final Answer:

Each square centimeter represents 25 square meters in the larger figure.

Do you want more details or have any questions?

Here are some related questions for practice:

1. If the scale was $1 \, \text{cm} = 10 \, \text{m}$, how would that affect the area ratio?
2. How many square meters does 2 cm² represent in the larger figure with the given scale?
3. What is the total perimeter of the larger figure if the smaller one has a perimeter of 28 cm?
4. What would be the area of the smaller figure if its length and width were halved?
5. How would the total area change if the scale changed to $1 \, \text{cm} = 3 \, \text{m}$?

Tip: Always square the scale factor when converting between areas!