The area of the actual backyard for which the scale model uses a scale in which 2 cm represents 1. 6 meters is 30.72 m².
Scale factor is the factor which is used to enlarge or smaller the original figure.
Scale factor is the ratio of representation measurement of the figure to the original figures.
The scale model uses a scale in which 2 centimeters represents 1.6 meters. The scale factor for this is,
[tex]r=\dfrac{1.6}{2}[/tex]
A scale model drawing of a backyard is 6 centimeters wide and 8 centimeters long. Thus, the length of the backyard will be,
[tex]L=\dfrac{1.6}{2}\times8\\L=6.4\rm \; m[/tex]
The width of the backyard will be,
[tex]W=\dfrac{1.6}{2}\times6\\W=4.8\rm \; m[/tex]
The area of the actual backyard, which is rectangular in shape is equal to the product of its length and width. Thus, the area of the backyard is,
[tex]A=6.4\times4.8\\A=30.72\rm \; m^2[/tex]
Hence, the area of the actual backyard for which the scale model uses a scale in which 2 cm represents 1. 6 meters is 30.72 m².
Learn more about the scale factor here;
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