1. **Problem statement:** We have two triangles, $\triangle FOR$ and $\triangle FAN$, where $\overline{OR} \parallel \overline{AN}$. Given $OR = 11.2$ units, $FO = 7$ units, $FN = 10$ units, and $FO = FR$ (isosceles triangle $FOR$), find the length of $AN$. 2. **Key concept:** Since $OR \parallel AN$, triangles $FOR$ and $FAN$ are similar by the AA similarity criterion (corresponding angles are equal). 3. **Set up similarity ratios:** Corresponding sides are proportional: $$\frac{FO}{FN} = \frac{OR}{AN}$$ 4. **Substitute known values:** $$\frac{7}{10} = \frac{11.2}{AN}$$ 5. **Solve for $AN$:** $$AN = \frac{11.2 \times 10}{7}$$ 6. **Calculate:** $$AN = \frac{112}{7} = 16$$ 7. **Final answer:** $$AN = 16.00$$ units (rounded to the nearest hundredth).