Definition
Dimension
A dimension is an independent direction in which a figure can extend or be measured.
What it means
Count the different directions needed to describe the figure. A line needs one direction. A flat rectangle needs two. A box needs three. Measurements such as 8 cm long, 3 cm wide, and 2 cm high tell how far the box extends in each direction.
Remember it
1D goes along; 2D adds across; 3D adds a third independent direction.
Example
A cuboid is 8 cm long, 3 cm wide, and 2 cm high. It is three-dimensional, and its three listed dimensions are 8 cm, 3 cm, and 2 cm.
Watch for
Making a square larger does not give it another dimension; it is still a flat two-dimensional shape.
Common mix-up
The number of dimensions tells how many independent directions there are; the measurements called dimensions tell the size in those directions.
Exact meaning
A dimension is an independent direction of extension or measurement. A line is one-dimensional, a flat figure is two-dimensional, and an ordinary solid is three-dimensional. The word can also name a measurement in one such direction, such as length, width, or height.