Exercise 4. Let ABCD 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 4: Let's cut the rectangle ABCD into isometric right triangles, as shown below. All 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_06_04_ba585959d2e020eaf8cbg-3.jpg?height=364&width=739&top_left_y=520&top_left_x=693)

Grader's Comment: The exercise was generally well done. However, a significant number of submissions presented reasoning without any supporting figures, which hinders grading and often leads to multiple confusions. An explicit figure was sometimes worth more than a long discourse.

Furthermore, a surprising number of students immediately considered the special case where the rectangle is a square or has dimensions $4 \times 1$, which is a pity because the solution to this special case is the same as the general case.