There are 7 similarly shaped figures in a set. the largest figure is 7 inches tall. each of the other figures is 1 inch shorter than the next larger figure.  the surface area of the largest figure is 588 in. squared. what is the  surface area of the smallest figure?

The first thing we must do for this case is to find the scale factor based on the dimensions of the figures.
 The largest figure is 7 inches tall. Each of the other figures is 1 inch shorter than the next larger figure.
 We have then that the smallest figure has a height of 1 inch.
 The scale factor is:
 k = (smallest figure) / (largest figure) = 1/7
 k = 1/7
 The surface area of the smaller figure is:
 A = k ^ 2 * (A ')
 Where
 A ': surface area of the largest figure.
 Substituting:
 A = (1/7) ^ 2 * (588)
 A = 12 in ^ 2
 
 The surface area of the smallest figure is:
 A = 12 in ^ 2

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