Counting Rectangles

Difficulty: Medium · Topics: Discrete Mathematics, Combinations, Geometry

Square ABCD is divided into 16 equal squares.

graph "x":[-0.7,4.7],"y":[-0.7,4.7],"axes":false,"ink":true,"label":"Square ABCD divided into a 4 by 4 grid","items":["type":"line","from":[0,0],"to":[4,0],"ink":true,"width":1.2,"type":"line","from":[0,1],"to":[4,1],"ink":true,"width":1.2,"type":"line","from":[0,2],"to":[4,2],"ink":true,"width":1.2,"type":"line","from":[0,3],"to":[4,3],"ink":true,"width":1.2,"type":"line","from":[0,4],"to":[4,4],"ink":true,"width":1.2,"type":"line","from":[0,0],"to":[0,4],"ink":true,"width":1.2,"type":"line","from":[1,0],"to":[1,4],"ink":true,"width":1.2,"type":"line","from":[2,0],"to":[2,4],"ink":true,"width":1.2,"type":"line","from":[3,0],"to":[3,4],"ink":true,"width":1.2,"type":"line","from":[4,0],"to":[4,4],"ink":true,"width":1.2,"type":"point","at":[0,0],"label":"A","anchor":"sw","ink":true,"type":"point","at":[4,0],"label":"B","anchor":"se","ink":true,"type":"point","at":[4,4],"label":"C","anchor":"ne","ink":true,"type":"point","at":[0,4],"label":"D","anchor":"nw","ink":true]

How many rectangles are there in the figure? (Squares count as rectangles.)