#3769. Why do we add the bases to find Area of a Trapezoid?

Mathematics, level: Middle
Posted Thu May 4 14:30:16 PDT 2006 by Donna Bucchiere (donna.bucchiere@acps.k12.va.us).
George Washington Middle School, Alexandria, VA
Materials Required: 2 trapezoid pattern blocks per student, ruler or centimeter paper
Activity Time: 45 minutes
Concepts Taught: Area of a Trapezoid and decomposing shapes

Prior knowledge of area of a parallelogram should be established.To start, each student is given two trapezoid pattern blocks, centimeter grid paper, and a ruler, and asked if they can calculate the area of one of the trapezoids by using both of them (encourage them to place the two trapezoids together to form a parallelogram). After they form the parallelogram with the two trapezoids have them calculate it's area (base of the first trapezoid plus base of the second trapezoid times height). Remind them that the original question posed was to calculate the area of one trapezoid. The students will now have to divide the area of the parallelogram by two. Thus the area of a trapezoid has been discovered.(1/2 X the sum of the bases X height)