Task# Area of a Trapezoid

Illustrative MathematicsVaries

The purpose of this task is for students to use the Pythagorean Theorem to find the unknown side-lengths of a trapezoid in order to determine the area. This problem will require creativity and persistence as students must decompose the given trapezoid into other polygons in order to find its area. In the solution provided, perpendiculars from A and B are drawn to the base and then the Pythagorean theorem is used to find the missing segment lengths. Alternatively, could be extended and perpendiculars can be drawn from and to this extended segment, giving a rectangle from which two triangles need to be subtracted to get trapezoid.