Why does the area of a square quadruple when you double the dimensions?

Answer 1

That's true for any rectangle, not just a square. Here's why:

The original area of any rectangle is (original length) times (original width).

When you double the dimensions, the new area is (2 x original length) times (2 x original width).

You learned a long time ago that when you're multiplying numbers, it doesn't make any

difference what order they're arranged in. So we'll take that formula for the new area,

and rearrange it in a different order:

(2 x original length) times (2 x original width) = (2 x 2) times (original length x original width).

The stuff inside the first parentheses multiplies to give the number ' 4 '.

The second parentheses enclose (original length x original width), and that's just

the original area. So the new area is (4) times (original area).

Quod erat demonstrandum.