5. (7 points) From the midpoint of each side of an acute-angled triangle with area $S$, perpendiculars are drawn to the other two sides. Find the area of the hexagon bounded by these perpendiculars.
Answer: $\frac{S}{2}$.

## Solution.

![](https://cdn.mathpix.com/cropped/2024_05_06_06b9f4bfa48aaf5de920g-3.jpg?height=474&width=952&top_left_y=1668&top_left_x=540)