Problem
The outline's left side and bottom are each 3 edges long, plus 6 step edges — 12 edges in total.
Walking around the boundary and counting each 16-cm edge turns the staircase shape into a simple count.
3.MD.D.8Draw A DiagramEach of the 12 outline edges is 16 cm: 12 × 16 = 192.
Multiplying the edge count by the edge length gives the whole heavy outline at once.
3.OA.C.7Identify SubproblemsThe regular hexagon's 6 equal sides have the same total length 192 cm, so divide by 6 to get one side.
Equal perimeters mean the hexagon's six equal sides share the same total, so each side is one sixth of it.
3.MD.D.8Identify SubproblemsOne side of the regular hexagon — the blank — is the whole staircase perimeter shared equally among the hexagon's six sides.
The hexagon is regular, so its six sides are all the same length, and its whole outline is just six copies of that one side length.
The hexagon's outline splits into its six side pieces with no gaps or overlaps, so those pieces add back up to the whole outline.
Six equal sides is six equal groups of one side length, which is exactly what six times that length means.
That whole hexagon outline is the same length as the staircase outline, because the two heavy outlines are given as equal and the staircase outline was already found to be 192 cm.
Finding the one side length that six copies build up to 192 cm is undoing a multiplication by six, and dividing by six is exactly that undoing.
This only needs Grade 3 perimeter sense: count the edges, multiply, then share the total over the hexagon's 6 sides!