2005 AMC 10A Problems/Problem 8
In the figure, the length of side of square is and =1. What is the area of the inner square ?
We see that side , which we know is 1, is also the shorter leg of one of the four right triangles (which are congruent, I'll not prove this). So, . Then , and is one of the sides of the square whose area we want to find. So:
So, the area of the square is .