A mathematics classroom that reflects the vision of NCTM's "Principles and Standards for School Mathematics" will have the teacher posing problems, asking questions that build on students' thinking, and encouraging students to explore different solutions. In teaching about area, it is not sufficient to give students the pertinent formulas and have them merely compute the areas of various polygons. The students should develop an understanding of the concept of area so that they can reason about the relationships between shapes to determine area. According to the Common Core State Standards for Mathematics, students in sixth grade should be able to find the area of special quadrilaterals by composing them into rectangles or decomposing into triangles and other polygons. The Common Core Standards for Mathematics Practice also describe how students should construct viable arguments and critique the reasoning of others. The activity presented in this article can be used when the students are being introduced to the areas of special quadrilaterals, especially trapezoids. Before students engage with this task, the authors suggest that they explore and develop the formulas for the areas of triangles, rectangles, and parallelograms and gain some experience decomposing and recomposing polygons. Alternatively, the activity may be approached as forging the connections between the various geometric and algebraic representations, making it a more advanced task suitable for high school students.