 This fact can be used to show that Area("w") is the smallest number of 2-cells in a van Kampen diagram over (∗) with boundary cycle labelled by "w".An "isoperimetric function" for a finite presentation (∗) is a monotone non-decreasing function
such that whenever "w" ∈ "F"("X") is a freely reduced word satisfying "w" = 1 in "G", then
where |"w"| is the length of the word "w".Then the "Dehn function" of a finite presentation (∗) is defined as