Problem
The left side AB is 10 cm, and the dividing segment MN is the same height as the rectangle, so MN = 10 cm.
MN runs from the top edge to the bottom edge, so it is exactly as tall as the rectangle.
4.G.A.1Draw A DiagramThe right part MDCN is a square, so all its sides are equal. Its side MN is 10 cm, so MD = 10 cm.
A square's four sides are all the same length, so once one side is 10 cm they all are.
4.G.A.2Identify SubproblemsThe top side MD of the right square MDCN is 10 cm long.
MD and MN are two sides of the same square MDCN that meet at corner M, and those two sides have the same length.
Folding the square across corner M lays side MD exactly on top of side MN, so the two sides must be equal in length.
MN is 10 cm because it is the side of the left rectangle AMNB directly across from AB, and AB is marked 10 cm.
MN and AB are opposite sides of the rectangle AMNB, and opposite sides of a rectangle have the same length.
Folding the rectangle so edge AB swings over onto segment MN lands one exactly on the other, so they are equal in length.
Since MD equals MN and MN equals 10 cm, MD has to be 10 cm as well.
The top of the big rectangle is AM plus MD.
The whole top edge is just the two top pieces laid end to end.
4.MD.A.3Identify SubproblemsThe rectangle is 14 cm wide and 10 cm tall, so the perimeter is two widths plus two heights.
Going all the way around a rectangle covers each of the two lengths and two widths exactly once.
4.MD.A.3Identify SubproblemsSpot the square to fill in the missing length, then go around the rectangle: it only needs Grade 4 perimeter sense!