In Session 6, we found the areas of different polygons (parallelograms, triangles) by dissecting the polygons and rearranging the pieces into a recognizable simpler shape.
In this case, we transformed a parallelogram into a rectangle by slicing a triangle off one end and sliding it along to fit into the other end. In doing so, we established that the area of the parallelogram was the same as the area of the equivalent rectangle (its base multiplied by the perpendicular height). Can we use the same technique and transform a circle into a rectangular shape?
Use a compass and draw a large circle. Fold the circle in half horizontally and vertically. Cut the circle into four wedges on the fold lines. Then fold each wedge into quarters. Cut each wedge on the fold lines. You will have 16 wedges.
Tape the wedges to a piece of paper to form the following figure:
Notice that we have a crude parallelogram with a height equal to the radius of the original circle and a base roughly equal to half the circumference of the original circle.