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 the following Interactive Activity to measure a circle and the resulting figure when you cut it into wedges and tape them together to form a crude parallelogram.
This activity requires the Flash plug-in, which you can download for free from Macromedia's Web site. A non-interactive version of this activity is available.
Notice that we have a crude parallelogram with a height equal to the radius of the original circle.