Final answer:
The question does not provide enough information to calculate the total square footage of a home. Calculating square footage typically requires multiplying the length and width of each room, or in the case of scale drawings, applying a scale factor to determine actual dimensions. Examples were given on how to apply scale factors to find the area of an actual carpet from a scale drawing and the wingspan of a model airplane.
Step-by-step explanation:
To determine the total square footage of a home from the context provided, further information would be necessary as the question, as presented, does not include sufficient data to calculate the area. Usually, the square footage is calculated by multiplying the length and width of each room and then summing up these areas for the entire home. In cases where scale drawings or scale factors are involved, the actual dimensions can be determined by applying the given scale factor to the measurements obtained from the drawing or model.
For instance, if a rectangular carpet is represented in a scale drawing with a scale factor of 1/24, and you want to find the carpet's actual area, you would measure the length and width on the drawing, multiply both by 24, and then calculate the area using the formula Area = Length × Width.
Regarding the example concerning the small airplane with a 16-foot wingspan and a model with a scale factor of 1/48, to find the model's wingspan in inches, you would write the scale factor as a ratio (1/48), and use this to calculate the model's wingspan by multiplying the actual wingspan by the inverse of the scale factor:
Wingspan of the model = Actual wingspan × Scale factor
= 16 feet × (1/48)
= 1/3 foot
= 4 inches
This process uses mathematical concepts from geometry and proportional reasoning to scale measurements up or down as needed.