In this Paper, we introduce Convergence of α-Cut. We define at Which point the α-Cut converges to the fuzzy numbers and it will be illustrated by example using dual trapezoidal fuzzy number and some mensuration problems are illustrated with approximated values. In this paper, we introduce Dual trapezoidal fuzzy numbers with its membership functions and its applications. Section one presents the introduction, section two presents the basic definition of fuzzy numbers section three presents Dual trapezoidal fuzzy numbers and its applications and in the final section we give conclusion.