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 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-6.jpg?height=349&width=724&top_left_y=514&top_left_x=690)

Grader's Comment Exercise was generally well done. However, a significant number of papers propose a reasoning without any supporting figure, which hinders grading and is often accompanied by several confusions. An explicit figure was sometimes worth more than a long discourse.

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