Problem
A square has 4 equal sides, so divide the perimeter by 4: 32 ÷ 4 = 8 cm.
Perimeter of a square is 4 equal sides; dividing recovers one side, a Grade 3 perimeter skill.
3.MD.D.8Work BackwardsThe top side (8 cm) = radius + 4 cm middle + radius, so the two radii together: 8 - 4 = 4 cm.
Each corner arc starts one radius from the vertex, so the leftover length is two radii.
3.MD.D.8Draw A DiagramOn the top side, the length left after the 4 cm straight middle is exactly the two corner radii, because the side runs one radius, then the 4 cm middle, then one more radius.
The top side is one straight length made of three touching pieces with no gap and no overlap -- the left corner reach, the 4 cm middle, and the right corner reach -- so those pieces add back to the whole side.
Each corner reach is exactly one radius, because it runs from the vertex out to the point where that vertex's quarter circle crosses the side, and that point lies on the circle, one radius from its center.
The two radii together are 4 cm, so one radius is half of that: 4 ÷ 2 = 2 cm.
Two equal radii share the leftover 4 cm equally, so halve it.
3.OA.C.7Draw A DiagramEach side is radius + straight part + radius -- take away the middle and split in two, easy Grade 3 perimeter thinking!