The area of rectangle A'B'C'D' is 32 square feet
Step-by-step explanation:
A dilation is a transformation that produces an image that is the 
same shape as the original, but is a different size
A dilation stretches or shrinks the original figure
The figure and its image after dilation are similar
If two rectangles are similar, then
∵ Rectangle ABCD is dilated to create rectangle A'B'C'D' 
∴ Rectangle ABCD is similar to rectangle A'B'C'D'
∵ The width of rectangle ABCD is 12 feet
∵ The width of rectangle A'B'C'D' is 8 feet
∴ 
- Simplify the ratio to its lowest term by divide up and down by 4
∴ 
∴ The scale factor of dilation is 
Let us use the rule of the similar rectangles above
∵ The area of rectangle ABCD is 72 square feet
∵ 
∴ 
∴ 
- By using cross multiplication
∴  × 9 = 72 × 4
 × 9 = 72 × 4
∴ 9  = 288
 = 288
- Divide both sides by 9
∴  = 32 feet²
 = 32 feet²
∴ The area of rectangle A'B'C'D' = 32 feet²
The area of rectangle A'B'C'D' is 32 square feet
Learn more:
You can learn more about area of shapes in brainly.com/question/6530759
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