Expert: Josh - 2/13/2007

Question
i am confused about this problem, and i need help please!!!!
it says: two similar polygons have a scale factor of 5:2. the area of the larger polygon is 100.find the area of the smaller polygon.

well i know that the rations of areas is the scale factor squared so
5:2 squared = 25:4  and the area of large polygon is 100 so 25:4=100:x
25x4=100 and 4x4=16 so i think the smaller polygons area =16.
.....is my answer correct?

Answer
Hi Mariah,

Your reasoning is correct.

The answer depends on what the scale factor refers to.
Assuming that it refers to the ratio between the side of the larger polygon to that of the smaller polygon, then, we certainly have to square this ratio, before we can compare the area between the two polygons.

This is due to the fact that the area of a regular polygon is given by 0.5*a*p, where a represents the apothem, and p denotes the perimeter (see http://regentsprep.org/Regents/math/farea/AreaRef.htm). Since these two parameters are linear, the area (their product) has quadratic dimension.

On the other hand, if the scale factor already refers to the area, then, the smaller polygon is 2/5 times the larger one in area.