1. **Problem Statement:** Find the perimeter of the polygon formed by three hexagons arranged together, where one side length is given as 5.75 meters. The dotted lines represent internal segments and do not count toward the perimeter. 2. **Understanding the shape:** Each hexagon is regular, so all sides are equal to 5.75 m. 3. **Formula for perimeter of a regular hexagon:** $$\text{Perimeter} = 6 \times \text{side length}$$ 4. **Calculate perimeter of one hexagon:** $$6 \times 5.75 = 34.5 \text{ meters}$$ 5. **Arrangement of three hexagons:** When three hexagons share sides, some sides are internal and do not count toward the perimeter. 6. **Counting the perimeter sides:** - Each hexagon has 6 sides. - Total sides for 3 hexagons: $3 \times 6 = 18$ sides. - Shared sides between hexagons are internal and excluded. 7. **Number of shared sides:** Three hexagons arranged together share 3 sides internally (each pair shares one side). 8. **Calculate the polygon perimeter:** $$\text{Perimeter sides} = 18 - 2 \times 3 = 12$$ (Each shared side is counted twice in total sides, so subtract twice the number of shared sides.) 9. **Final perimeter:** $$12 \times 5.75 = 69 \text{ meters}$$ **Answer:** The perimeter of the polygon is **69 meters**.