# In the figure below, the side length of of the smaller square is 4, and the area of the red region is 1. What is the area of the larger square?

I already did some progress and labeled some similar segments.

The red triangle has area $$1$$ but it has base and height $$x$$ so the area will be $$x^2/2=1$$ so $$x^2=2$$ and finally $$x=\sqrt 2$$. By the Pythagorean theorem we also have that $$y^2=x^2+4^2=4^2+\sqrt 2^2=18$$. But $$y^2$$ is just the area of the larger square since it's the side lenght squared. So the area will be $$18$$