Question

The scale factor of the blueprint of a shopping mall to the actual shopping mall is 1 in/18 ft. The area of the mall on the blueprint is 190 in². What is the area of the actual shopping mall?

1) 6,840 ft²
2) 36,118 ft²
3) 3,420 ft²
4) 61,560 ft²

Answer 1

To calculate the area of the actual shopping mall from the blueprint, we square the scale factor and multiply by the blueprint area. By applying the scale factor of 1 in/18 ft, the resulting area is 61,560 ft².

Step-by-step explanation:

Calculating the Area of the Actual Shopping Mall

To find the area of the actual shopping mall from the scaled blueprint, we need to consider the scale factor. The scale factor provided is 1 inch to 18 feet. First, we convert inches to feet to match the units. Since the area on the blueprint is 190 in², we must square the scale factor to convert the area. The scale factor squared is (1 in./18 ft.)² or (1/18)² square inches per square foot. To calculate the actual area, we multiply the blueprint area by the square of the scale factor:

1. 
   
3. Convert the scale factor from inches to feet: (1 in.)²/(18 ft.)² = (1 in./12 ft.)².
4. 
   
6. Square the scale factor: (1/18)^2 = 1/324 square feet per square inch.
7. 
   
9. Multiply the blueprint area by the square of the scale factor: 190 in² * 1/324 ft²/in² = 61,560 ft² (since 18 inches² = 1 feet², 190*324 = 61,560).

Therefore, the area of the actual shopping mall is 61,560 ft².