Question

A square is inscribed within another square by connecting the midpoints of the larger square. The edge length of the outer square is x. Express the area of the inner square as a function of x.

Answer 1

Each edge of the inner square has a length of √[(x/2)²+(x/2)²]=√2x²/4=(x√2)/2
Then, the area is 2x²/4=x²/2 ☺☺☺☺