Exercise 3. On a rectangular box with dimensions $6 \mathrm{~cm} \times 4 \mathrm{~cm}$, a ribbon has been placed diagonally as shown in the figure below (the ribbon is represented in gray in the figure).

![](https://cdn.mathpix.com/cropped/2024_06_04_e23d725cd2c5ceb81650g-2.jpg?height=320&width=404&top_left_y=518&top_left_x=858)

We measured $A B=1 \mathrm{~cm}$ and $B C=5 \mathrm{~cm}$. Calculate the width of the ribbon.
Solution to Exercise 3 To find the width of the ribbon, we will calculate the area $\mathcal{A}$ of the trapezoid $A B C D$ in two different ways. The area of a trapezoid is base $\times$ height. Taking the base $C D$, we find $\mathcal{A}=1 \times 4=4 \mathrm{~cm}^{2}$. If $l$ is the width of the ribbon, by calculating $\mathcal{A}$ with the base $B C$, we find $\mathcal{A}=5 \times l$. We deduce that $l=\frac{4}{5}$.