Problem
Looking at the solid from below, 9 of the 11 cubes rest on the floor and 2 are stacked on top of floor cubes. The 9 floor squares form an L-shape: a top row of 6 unit squares and, under its left 3 squares, a bottom row of 3 unit squares.
Telling apart the flat floor shape (2D) from the stacked cubes (3D) is the kindergarten idea of two- vs three-dimensional shapes.
K.G.A.3Visualize Spatial RelationshipsDrawing the L-shape on grid paper: it fits inside a 6 cm by 2 cm rectangle, with a 3 cm by 1 cm notch missing from the bottom-right. Each side of every unit square is 1 cm.
Sketching the flat outline turns a 3D puzzle into a simple polygon-perimeter problem at the Grade 3 level.
3.MD.D.8Draw A DiagramWalk the outline of the L-shape, counting 1-cm edges: across the top is 6, down the right is 1, left along the step is 3, down 1, left along the bottom is 3, and up the left side is 2. Adding these gives the perimeter.
For an L made of two rectangles, the inner step lengths slide together so the perimeter equals that of the 6 by 2 bounding rectangle: 2 x (6 + 2) = 16.
4.MD.A.3Identify SubproblemsWalking the outline of the L-shaped floor figure and adding its 1-cm edges gives a perimeter of 16 cm.
The perimeter is the whole distance around the figure, and that outline is one closed path cut into straight runs that meet end to end with no gaps or overlaps, so its total length is those run lengths added together.
Each straight run lies along the sides of the unit squares, and every square side is exactly 1 cm, so a run's length is simply how many of those 1-cm sides lie along it.
Laying that many 1-cm sides in a straight line makes that many equal lengths of 1 cm, which measures that many centimeters.
Look at the solid from underneath, draw the flat shape it sits on, then add the outside edges - an L-shape's perimeter matches its bounding box!