23) On a sheet of Carlo's notebook, there is a rectangle with two yellow sides of $24 \mathrm{~cm}$ and two red sides of $36 \mathrm{~cm}$. Carlo colors every point of the rectangle the same color as the nearest side to that point. What will be the area of the part of the rectangle colored yellow?
(A) $144 \mathrm{~cm}^{2}$,
(B) $288 \mathrm{~cm}^{2}$
(C) $364 \mathrm{~cm}^{2}$,
(D) $442 \mathrm{~cm}^{2}$,
(E) $524 \mathrm{~cm}^{2}$.
23. The answer is $(\mathbf{B})$.

Referring to the figure, the points of the rectangle for which the nearest side is one of the two longer sides of $24 \mathrm{~cm}$ are those belonging to the isosceles triangles $A E D$ and $B C F$, which are right-angled at $E$ and $F$ respectively. The length of $D E$ is $\frac{24}{\sqrt{2}} \mathrm{~cm}$, and thus the area of $A E D$ is $\frac{24^{2}}{4} \mathrm{~cm}^{2} = 144 \mathrm{~cm}^{2}$, and this is also the area of $B C F$. Therefore, the measure of the part of the sheet colored yellow is $=288 \mathrm{~cm}^{2}$

![](https://cdn.mathpix.com/cropped/2024_04_17_1da74e1307acd0f8cf0eg-6.jpg?height=577&width=845&top_left_y=2027&top_left_x=660)