Exercise 11. Let $A B C D$ be a rectangle with area 4. Let I be the midpoint of $[A D]$ and let $J$ be the midpoint of $[B C]$. Let $X$ be the point of intersection of (AJ) and (BI), and let Y be the point of intersection of (DJ) and (CI). What is the area of the quadrilateral IXJY?
Solution to Exercise 11 Let's cut the rectangle $A B C D$ into isometric right triangles, as shown below. All the triangles have the same area, and the rectangle is made up of 16 triangles in total: each triangle therefore has an area of $1 / 4$. The quadrilateral IXJY is formed of 4 triangles. Its area is therefore equal to 1.

![](https://cdn.mathpix.com/cropped/2024_04_29_73269b600131539d27eeg-6.jpg?height=349&width=721&top_left_y=514&top_left_x=694)