Two-Square Illusion

Find area of inner square

If the area of the outer square is 100, what is the area of the inner square?
You don't need a calculator. Click or scroll down to see the solution.

Looks flat     Looks like a cube

First, rotate the inner square 45 degrees, then divide the outer square into four equal parts.
The inner square overlaps one-half of each of the four parts of the outer square.
Therefore the inner square is one-half the area of the outer square, or 50.

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Revised: December 28, 2007