16) The three lines drawn each divide the entire figure into two parts of equal area. Consider the hatched areas $A$ and $B$. Which of the following statements is true?

(A) $\operatorname{area}(A)>\operatorname{area}(B)$

(B) $\operatorname{area}(A)=\operatorname{area}(B)$

(C) $\operatorname{area}(A)<\operatorname{area}(B)$

(D) the figure is impossible

(E) no conclusion can be drawn.

![](https://cdn.mathpix.com/cropped/2024_04_17_807214d42c092eaa073dg-2.jpg?height=283&width=377&top_left_y=1604&top_left_x=1087)
16) The answer is $(\mathbf{C})$. Remove the vertical segment from the drawing and let $A^{\prime}$ be the area of the figure obtained on the left side. Since we know that area $\left(A^{\prime}\right)+\operatorname{area}(X)=\operatorname{area}(B)+\operatorname{area}(Y)$ and that area $\left(A^{\prime}\right)+\operatorname{area}(Y)=\operatorname{area}(B)+\operatorname{area}(X)$, we deduce that area $\left(A^{\prime}\right)=\operatorname{area}(B)$. Since the vertical segment cuts the region indicated with $A$ in the text, we have area $(A)<\operatorname{area}\left(A^{\prime}\right)$ and therefore

![](https://cdn.mathpix.com/cropped/2024_04_17_b7bd426b053cce897cc3g-2.jpg?height=307&width=420&top_left_y=1668&top_left_x=1514)
$\operatorname{area}(A)<\operatorname{area}(B)$.