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 735 in.2. What is the surface area of the middle-sized 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

The surface area of the smallest figure is:

A = 12 in ^ 2

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