Area problem

In the Swiss journal there is a riddle about areas. The question is to find the area of the red quadrilateral. It should be added that the right square goes through the center of the left one. Here is a reformulated question:

"A square of side length 5 is placed with one of its corner at the center of square of side length 4 so that one of the sides of the later is cut at a ratio of 3:1. What is the area of the intersection?"

It is a beautiful example on how additional information can confuse. There is no computation and no integration needed for this problem.