An important message teachers convey to their students is that mathematics is founded on reasoning and is not just a collection of rules to apply. Many mathematical rules such as area formulas can be derived in ways that are age-appropriate to students, and it is an important part of mathematics education that students engage in these derivations to some extent. A review of several Australian Year 8 textbooks showed that they generally included the reasoning behind the area formulas (Stacey & Vincent, 2008). For the area of the trapezium, there was a surprising variety of methods. In this article, the authors illustrate five methods for finding the area of the trapezium, which many students will enjoy discovering these variations on a theme. The authors stress that, by exposing students to a variety of dissection methods and encouraging them to find their own variations, teachers promote flexible thinking, greater understanding and less reliance on memorised area formulas. (Contains 5 figures.)