Question

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?

Answer 1

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
Answer:
The surface area of the smallest figure is:
A = 12 in ^ 2