Final answer:
The 4-foot by 8 feet model train display represents an actual area of 819,200 square feet when using a scale factor of 1:160 to convert the model dimensions to real-life dimensions.
Step-by-step explanation:
To calculate the actual area that the model train display represents, we need to apply the scale factor to the dimensions of the model. The scale factor is given as 1:160, meaning that 1 unit on the model represents 160 units in real life.
The model's dimensions are 4 feet by 8 feet. To find the actual area the display represents, follow these steps:
- Convert the model dimensions from feet to the equivalent scale in real life by multiplying each dimension by the scale factor. So, 4 feet × 160 = 640 feet and 8 feet × 160 = 1280 feet.
- Calculate the actual area by multiplying these converted dimensions: 640 feet × 1280 feet = 819,200 square feet. This is the area the display represents in real life.
Therefore, a 4-foot by 8-foot model train display on a 1:160 scale represents an actual area of 819,200 square feet.