Question

5 on a map with a scale of 1 inch to 12 feet, the area of a restaurant is 60 in². han says that the actual area of the restaurant is 720 ft². do you agree or disagree? explain your reasoning.

Explanation:

Step1: Recall scale for area

For a scale of \(1\) inch to \(12\) feet, the scale factor for length is \(1:12\). For area, the scale factor is the square of the length scale factor, so \((12)^2 = 144\) (since area is a two - dimensional measurement, we square the linear scale factor).

Step2: Calculate actual area

The area on the map is \(60\space in^2\). To find the actual area, we multiply the map area by the area scale factor. So the actual area \(A=60\times144\) square feet.
Calculate \(60\times144 = 8640\space ft^2\).

Step3: Compare with Han's answer

Han says the actual area is \(720\space ft^2\), but we calculated the actual area as \(8640\space ft^2\), which is not equal to \(720\space ft^2\).

Answer:

I disagree with Han. The linear scale is \(1\) inch to \(12\) feet, so the area scale is \(1\space in^2\) to \(12\times12 = 144\space ft^2\). The actual area should be \(60\times144=8640\space ft^2\), not \(720\space ft^2\).