Question

practice using scale to find areas
study the exampie showing how to find an actual
area from a scale drawing. then solve problems 1 - 4.
example
a camping supply store uses a tent as its logo.
the store makes a sign with the logo on it. the scale
from the drawing of the logo to the logo on the sign
is 1 in. to 2 ft. what is the area of the logo on the sign?
you can use a scale factor to find the
a = 1/2 bh
= 1/2 (1.5 × 2)(1.5 × 2)
= 4.5
dimensions on the sign. the scale factor from
the logo to the sign is 2/1, or 2.
the area of the logo on the sign is 4.5 ft².
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 1:8.
what is the area of the logo on the shirts? show your work.
solution
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.
1n/ft 2/100
6 in = 300 ft
3.2 =

Explanation:

Step1: Find the actual length

The scale is \(2\) in. to \(100\) ft. For a \(6\) - in. length on the drawing, let the actual length be \(x\) ft. Set up a proportion \(\frac{2}{100}=\frac{6}{x}\). Cross - multiply: \(2x = 6\times100\), so \(x=\frac{6\times100}{2}=300\) ft.

Step2: Find the actual width

For a \(3.2\) - in. width on the drawing, let the actual width be \(y\) ft. Set up a proportion \(\frac{2}{100}=\frac{3.2}{y}\). Cross - multiply: \(2y=3.2\times 100\), so \(y = \frac{3.2\times100}{2}=160\) ft.

Step3: Calculate the area

The area formula for a rectangle is \(A = length\times width\). Substitute \(l = 300\) ft and \(w = 160\) ft. \(A=300\times160 = 48000\) \(ft^{2}\).

Answer:

The area of the section she will search is \(48000\) \(ft^{2}\).