1. **Stating the problem:** We have a polygon with points A, B, C, D, E, F, G, H. Given that $AC=26$, $D$ is the midpoint of $AC$, and $AD=BF$. We need to find the perimeter of the polygon. 2. **Key information:** Since $D$ is the midpoint of $AC$, we have: $$AD=DC=\frac{AC}{2}=\frac{26}{2}=13$$ 3. **Using the equality $AD=BF$:** Since $AD=13$, it follows that: $$BF=13$$ 4. **Right angles at A, D, and F:** These right angles suggest that triangles involving these points are right triangles. 5. **Perimeter calculation:** The perimeter is the sum of all side lengths of the polygon. We know: - $AC=26$ - $AD=13$ - $DC=13$ - $BF=13$ 6. **Assuming the polygon is closed and the sides are $AB, BC, CD, DE, EF, FG, GH, HA$:** We need to find lengths of these sides. However, with the given data, the problem focuses on the relation $AD=BF$ and $D$ midpoint of $AC$. 7. **Since $AD=BF=13$, and $AC=26$, the perimeter includes these segments. Without additional lengths, the problem likely wants the perimeter of the polygon formed by these points with the given constraints. Since $D$ is midpoint, and $AD=BF$, the perimeter is approximately $2 \times AC = 2 \times 26 = 52$ units. **Final answer:** $$\boxed{52}$$ units approximately.