
Subject: precalculus
Name: Kelly Boulton
Who is asking: Student
Level: Secondary
Question:
Two 12sided polygons are similar. A side of the larger polygon is 3 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.
Hi Kelly,
If the question was changed  and the two polygons were rectangles (or triangles) what would be the answer?
If you know the answer for two triangles, then you could imagine dividing one of the 12sided polygons into triangles, with some interior 'center' and comparing these triangles with the similar triangles in the other 12sided polygon.
If the ratio for each pair of similar triangles came out to be K, and we have the same number of triangles in each polygon, then the ratio of the areas of the polygons would also be K.
[Note I assume you are aware of the critical property that if I divide an area into nonoverlapping pieces, then the area of the whole is the sum of the areas of the pieces. This property is at the root of one of two basic process in calculus. It would not surprise me if your teacher is getting you ready for that type of reasoning  hence it IS precalculus!]
Cheers,
Walter Whiteley

