The two polygons above are similar. the scale factor of the smaller polygon to the larger polygon is 3. the area of the smaller polygon is 12 sq. units. what is the area of the larger polygon?

You would think it was 3 * 12 = 36. Not so. All polygons have to be broken down into some figure that will give 2 dimensions that are at right angles to each other. That would mean that
d1 * d2 = Area for the small polygon
3d1 * 3d2 = area of the larger polygon

What that means is that the area of the larger one is 9 times the smaller one.
Area large = 12 * 9 = 108 square units. <<<<< answer.

If you find this hard to be leave try it with a square.
Suppose you have a square (the small one) that is 3 cm by 3 cm
The small one has an area of 3*3 cm^2 = 9 cm

Now you have another square that is 3 times larger. That means that each side is 3*3 = 9
So s = 9
Area = s^2
Area = 9^2 = 81 cm^2
81 is 9 times larger than 9 just as you would think.