Problem
The square's area is 12 × 12 = 144 cm². The rectangle has the same area and a height of 9 cm, so its width is 144 ÷ 9 = 16 cm.
Area of a rectangle is width × height, so if you know the area and one side you divide to get the other — a Grade 3 area idea.
3.MD.C.7Identify SubproblemsThe rectangle is 16 cm wide.
The rectangle has to cover the same surface as the square, and the square's surface is twelve rows of twelve.
Laying that same surface out in rows 9 cm tall, the width is whatever makes nine equal rows fill it, and dividing is what undoes the multiplying.
The square juts 3 cm left of the rectangle, so the figure spans 3 + 16 = 19 cm along the bottom.
A quick picture shows the leftmost point is the square's left side and the rightmost point is the rectangle's right side, so the overall width is just the two pieces added.
3.MD.D.8Draw A DiagramOn a staircase each step right is matched on top and each step up on the side, so the perimeter is 62 cm.
On a staircase outline, every step you take to the right is matched by the top, and every step up is matched by the side, so the bent edges line up to the same total as a plain rectangle around it.
3.MD.D.8Draw A DiagramAn L-shaped outline has the same perimeter as the smallest box you can draw around it — the steps just slide to the edges.