USING A SCALE DRAWING TO FIND AREA

Similar shapes are proportional figures that have the same shape but not necessarily the same size.

A scale drawing is a proportional two-dimensional drawing that is similar to an actual object. Scale drawings can represent objects that are smaller or larger than the actual object.

A scale is a ratio between 2 sets of measurements. It shows how a dimension in a scale drawing is related to the actual object. Scales are usually shown as two numbers separated by a colon such as 1:20 or 1 cm:1 m. Scales can be shown in the same unit or in different units.

Example 1 : 

The art class is planning to paint a mural on an outside wall. This figure is a scale drawing of the wall. What is the area of the actual wall ?

Solution : 

Scale factor :

2 in : 3 feet -----> 1 in : 3/2 feet

Step 1 :

Find the length of the wall in feet. 

Length  =  28 inches

Length  =  28 x 3/2 feet

Length  =  14 x 3 feet

Length  =  42 feet

Step 2 :

Find the width of the wall in feet. 

Width  =  11 inches

Width  =  11 x 3/2 feet

Width  =  33/2 feet

Width  =  16.5 feet

Step 3 : 

Find area of the wall in square feet. 

Area of the wall  =  Length x Width 

Area of the wall  =  42 x 16.5

Area of the wall  =  693 square feet. 

Example 2 : 

David would like to make paint the rectangular shaped wall. The measures of dimensions of the wall is given in the picture using scale factor. In the picture given below, every 1 inch represents 3 feet of the actual length. If the cost of painting is $2.50 per square feet, find the total cost of painting for the entire wall. 

Solution : 

Scale factor : 1 in = 3 feet

Step 1 :

Find the length of the wall in feet. 

Length  =  8 inches

Length  =  8 x 3 feet

Length  =  24 feet

Step 2 :

Find the width of the wall in feet. 

Width  =  4 inches

Width  =  4 x 3 feet

Width  =  12 feet

Step 3 : 

Find area of the wall in square feet. 

Area of the wall  =  Length x Width 

Area of the wall  =  24 x 12

Area of the wall  =  288 square feet.  

Step 4 : 

Find the total cost of painting for the entire wall. 

Cost of painting per square feet  =  $2.50

Total cost of painting for the entire wall  is equal to area of the wall times $2.50

=  288 x 2.50

=  720

So, the total cost of painting for the entire wall is $720

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