Answer :
Final answer:
The area of Allen's scale model of a house at a 1:36 linear scale from an 1,800 square foot real house is 200 square inches.
Explanation:
The student has asked about building a scale model of a rectangular house. Given that the full-scale house has a square footage of 1,800 square feet, we must determine the area of Allen's scale model when it is built on a linear scale of 1:36. To do this, we first need to understand the concept of a scale factor and how it affects the area in a scale model. Since the scale is 1:36, this means that each unit of measurement on the model is 36 times smaller than the actual house.
To find the scale model area, we need to adjust the area proportionally. The area shrinks by the scale factor squared (since area is a two-dimensional measurement). The scale factor for length is 1/36, so the scale factor for the area is (1/36)^2 or 1/1296. We then multiply the actual area by the area scale factor: 1,800 square feet * 1/1296 = 1.38888... square feet in the scale model. However, we need the answer in square inches. Since 1 square foot equals 144 square inches (12 inches by 12 inches), we convert the model area to square inches: 1.38888 square feet * 144 square inches/square foot = 200 square inches. Therefore, the area of Allen's scale model in square inches is 200 square inches.
