Similar pyramids

1. Sep 12, 2009

IniquiTrance

1. The problem statement, all variables and given/known data

If I have similar pyramids each with similar triangular bases, how can I prove that the ratio of the area of the bases = the ratio of the heights of the pyramids squared?

Thanks!

2. Relevant equations

3. The attempt at a solution

2. Sep 12, 2009

Dick

If the pyramids are similar then the ratio of the heights is the same as the ratio of the sides of the base triangle. If you change all of the sides of the triangle by a constant ratio, how does the area change?

3. Sep 12, 2009

IniquiTrance

I'm not sure how to proceed...

4. Sep 12, 2009

IniquiTrance

I see that if the scaling factor is k, then the ratio of the areas is k2. But how does that relate to the height of the pyramids?

5. Sep 12, 2009

IniquiTrance

Hmm, I think I see it.

k equals the ratio of the sides of the bases which = the ratio of the heights. Squaring this equals the ratio of the areas.

Thanks!