A scale model of a rectangular building lot measures 7 feet by 5 feet. If the actual house will be built using a scale factor of 12, what is the area of the actual building lot?

35 square feet
420 square feet
840 square feet
5,040 square feet

1 answer

To find the area of the actual building lot, we first need to determine the dimensions of the actual lot based on the scale model dimensions and the scale factor.

The scale model measures:

  • Length = 7 feet
  • Width = 5 feet

Using a scale factor of 12, the actual dimensions of the building lot will be:

  • Actual Length = 7 feet × 12 = 84 feet
  • Actual Width = 5 feet × 12 = 60 feet

Next, we calculate the area of the actual building lot: \[ \text{Area} = \text{Length} \times \text{Width} = 84 \text{ feet} \times 60 \text{ feet} \] Calculating this: \[ \text{Area} = 84 \times 60 = 5040 \text{ square feet} \]

Thus, the area of the actual building lot is 5,040 square feet.