Very confusing word problem

Question

2 nine sided polygons are similar. A side of the larger polygon is 4 times as long as the corresponding side of the smaller polygon. What is the ratio of the area of the larger polygon to the area of the smaller polygon.

Answer 1

"Similar" means one is a scale model of the other.

 

If you increase all dimensions of ANY plane figure by a factor, the ratio of the areas is that factor squared!

 

Large dimension is 4x the small one.

The ratio is 16:1.

 

Try it with a couple of composite figures that are easier to work with.

Simple house: a rectangle with a triangle on top.

Same thing with a semicircle on top.

You can divide a nine-sided polygon into a bunch of similar triangles.  If you increase its size, every dimension increases by the same ratio.  You don't really need to do the calculations to see that the ratio of areas is ratio of dimensions squared.  Just look at any one of the triangles.

 

Answer 2

The ratio of the area is as the square of the scale of the linear measures.

For a polygon with sides 4 time larger the area is 16 times larger.

 

The ratio of the area of the larger to the smaller is 16 / 1.