In this study, a new method for ranking trapezial fuzzy numbers, generalized trapezoidal fuzzy numbers with different left and right heights, is presented. It considers triangles of a trapezium, a quadrilateral with no parallel sides, and uses the centers' of the nine-point circles and the areas of these triangles' to calculate the ranking score of the trapezial fuzzy number. The score of the trapezial fuzzy number is also expressed in terms of vertices of the trapezium. The method is simple and efficient, making the application of this method to real life problems more effective. The advantages of the proposed method are given with examples. Certain applications of the proposed ranking method to the fuzzy risk analysis problem, based on trapezial fuzzy numbers, are also presented. The proposed method ranks not only standardized, but also arbitrary trapezial fuzzy numbers. As a result, it is unnecessary to normalize to fuzzy numbers to apply the fuzzy risk algorithm.