Problem
Sliding each step outward keeps its length and straightens the outline into a 12 by 8 rectangle.
Sliding an edge sideways keeps it the same length, so the staircase outline can be straightened into the rectangle that hugs it.
3.MD.D.8Draw A DiagramSliding the steps outward turns the outline into a rectangle without changing any edge's length.
Sliding a segment carries it to a new place without stretching or bending it, so its length is exactly what it was.
The horizontal pieces slid up gather into the rectangle's top and the vertical pieces slid across gather into its side, so the same edges regroup into the four sides of the rectangle.
A rectangle's perimeter is twice the width plus twice the height. Add the width and height, then double the sum.
Two long sides and two short sides means you count each pair once and double it.
4.MD.A.3Identify SubproblemsThe two 9 cm notch segments poke inward and never join that rectangle, so add 9 x 2 = 18 cm.
The notch adds real edge that you actually walk along, so it counts on top of the straightened rectangle.
3.MD.D.8Identify SubproblemsAdd the rectangle's perimeter and the two notch segments to get the full distance around the figure.
The perimeter is the straightened rectangle plus the extra edge that the notch adds.
3.MD.D.8Identify SubproblemsSlide the right-angle steps flat to get a rectangle, then add back any edge that pokes inward.