Given a square piece of paper, show how by creasing and folding only, a square of half the area of the original can be obtained.

Let the original square have side of length x.

Connect the midpoints of the original square to form a smaller interior square. The side of this interior square is sqrt((x/2)^2 + (x/2)^2) [Pythagorean Theorem] and the area is:

(x/2)^2 + (x/2)^2 = (x^2)/4 + (x^2)/4 = (x^2)/2 = half the area of the original square.

So just make the obvious folds and creases after connecting the midpoints of the original square.

 

 

 

 

Edited on April 8, 2004, 8:52 am

Posted by Penny on 2004-04-08 08:42:17