Question

practice using scales to find areas
1 employees of the store in the example wear shirts with the logo on the back. the scale from the original logo in inches to the logo on the shirt in inches is 1:6. what is the area of the logo on the shirt? show your work.
2 dr. gordon has a scale drawing of a building site. the drawing uses the scale 2 in. on the drawing for every 100 ft on the building site. dr. gordon marks a 6 in.-by-3.2 in. section of the drawing to show the section she will search. what is the area of the section she will search? show your work.

Explanation:

Step1: Find the scale factor for length

The scale is \(2\) in. for every \(100\) ft. So the scale factor \(k\) (inches to feet) is \(\frac{100}{2}=50\) (ft per inch).

Step2: Calculate the actual length and width

For the length \(l = 6\) in., the actual length \(L=6\times50 = 300\) ft.
For the width \(w = 3.2\) in., the actual width \(W=3.2\times50=160\) ft.

Step3: Calculate the area

The area formula for a rectangle is \(A = L\times W\). Substitute \(L = 300\) and \(W = 160\) into the formula: \(A=300\times160\).

Answer:

\(48000\) square feet