Problem
Top-left corner at the origin: the top row spans 27 cm across and 6 cm down, and the left column reaches 12 cm tall.
Putting the picture on a grid turns 'staircase' into clear straight edges I can measure.
4.MD.A.3Draw A DiagramHorizontal pieces: the top (27 cm), the step (27 - 9 = 18 cm), and the bottom (9 cm).
Grade 3 addition: the left-and-right edges of the outline add to 54 cm.
3.NBT.A.2Identify SubproblemsThe horizontal edges of the figure's outline add up to 54 cm.
The left-and-right run of the outline is three horizontal segments in a row — the 27 cm top, the 18 cm ledge where the top row juts past the lower rectangle, and the given 9 cm bottom of the lower rectangle — meeting end to end with no gaps or overlaps, so their lengths add to the whole horizontal distance.
Two of those segment lengths, 27 cm and 18 cm, are not given directly but come out of the picture.
The top segment is 27 cm because three rectangles, each 9 cm wide, stand side by side, so it is 9 cm counted three times.
The ledge is 18 cm because the top row's 27 cm underside is split by the lower rectangle into a covered 9 cm part on the left and the exposed ledge, and those two pieces must rejoin to the full 27 cm, leaving 18 cm.
Vertical pieces: the top row's right side (6 cm), the step drop (6 cm), and the tall left side (12 cm).
Grade 3 addition: the up-and-down edges of the outline add to 24 cm.
3.NBT.A.2Identify SubproblemsAdd the horizontal total and the vertical total to get the full distance around the figure.
Perimeter is just the whole trip around the edge: 54 cm across plus 24 cm up and down is 78 cm.
3.MD.D.8Identify SubproblemsTrace the outline once, adding every edge as you go, and the staircase perimeter is just 78 cm!