The problem presented states that a blueprint of a park has a scale of 1 centimeter to 20 meters, and the area of the playground on the blueprint is 8 square centimeters. The question asks to find the area of the actual playground in the park.

Solution:

Since the scale is 1 cm : 20 m, this means that every 1 cm on the blueprint represents 20 meters in the actual park.

1. The scale factor for length is 20 (since 1 cm on the blueprint equals 20 m in real life).

2. To find the scale factor for area, we square the length scale factor: $(20)^2 = 400$ Therefore, the area on the actual park is scaled by a factor of 400 compared to the area on the blueprint.

3. The area of the playground on the blueprint is given as 8 square centimeters. To find the actual area, we multiply the blueprint area by the area scale factor: $8 \, \text{cm}^2 \times 400 = 3200 \, \text{m}^2$

Thus, the area of the actual playground in the park is 3200 square meters.

Would you like any more details or have further questions?

Here are five related questions to deepen your understanding:

1. How would the solution change if the scale was 1 cm to 10 meters instead?
2. If the blueprint showed an area of 10 cm², what would be the actual area of the playground?
3. How does changing the scale affect the calculated area in real life?
4. If the blueprint had irregular shapes, how would you calculate their area in real life?
5. Can you explain the difference between scaling length and scaling area?

Tip:

Always square the scale factor when converting areas between maps and real-world dimensions.