Two-dimensional shapes have dimensions, such as length and width, while three-dimensional shapes have an additional dimension, such as height. Any shape that only has a surface area is a 2-D shape while shapes with volume are 3-D shapes.
By examining the units of area, inches-squared or an equivalent unit, it is clear that an area measurement is an example of a 2-D measurement. Likewise, volume is a 3-D measurement based on units of inches cubed. While the surface area of a 3-D shape can be determine, there is no volume to a 2-D shape. Only calculations or a lower order can be performed on any given shape.