6. Points $E$ and $F$ are the midpoints of sides $\overline{B C}$ and $\overline{C D}$ of rectangle $A B C D$. What is the area of triangle $A E F$ if the area of rectangle $44 \mathrm{~cm}^{2}$?
6. Sketch:

![](https://cdn.mathpix.com/cropped/2024_05_30_7e3b3cfdf053042fa10ag-06.jpg?height=434&width=554&top_left_y=754&top_left_x=380)

1 point

Let \( a \) and \( b \) be the lengths of the sides of the rectangle; \( |AB| = a, |BC| = b \).

We have:

\[
\begin{array}{rlrl}
p_{\triangle A D F} & =\frac{1}{2} \cdot b \cdot \frac{a}{2}=\frac{a b}{4}, & & 1 \text{point} \\
p_{\triangle A B E} & =\frac{1}{2} \cdot a \cdot \frac{b}{2}=\frac{a b}{4}, & \\
p_{\triangle E C F} & =\frac{1}{2} \cdot \frac{b}{2} \cdot \frac{a}{2}=\frac{a b}{8} & & \text{point} \\
p_{\triangle A E F} & =p(ABCD)-\left(p_{\triangle A D F}+p_{\triangle A B E}+p_{\triangle E C F}\right) & & 1 \text{point} \\
& =a b-\left(\frac{a b}{4}+\frac{a b}{4}+\frac{a b}{8}\right) & 1 \text{point} \\
& =a b-\frac{5 a b}{8} & 1 \text{point} \\
& =\frac{3 a b}{8} & 1 \text{point} \\
& =\frac{3}{8} \cdot 44 & 1 \text{point} \\
& =16.5 \text{ cm}^2 & & 1 \text{point} \\
& & 1 \text{point}
\end{array}
\]