Finding the area of a parallelogram that is not a rectangle presents a challenge because the unit squares are going to be cut at an angle, making them difficult to carefully count. However, if we cut along the height of the parallelogram, the resulting pieces can be rearranged to form a familiar shape: a rectangle. We know the rearranged shape is a rectangle because:

• the slanted sides of the parallelogram have the same length and slope so they fit together exactly and form a quadrilateral,

• the height is perpendicular to the base so the top two corners are right,

• the side opposite the base is parallel so the left bottom corner is right, and

• consecutive  angles of a parallelogram are supplementary so the left bottom angle less a right angle together with the bottom right angle will form a right angle. 

Note: The justification above for why the rearranged shapes form a rectangle is provided for completeness. At the middle school level, this deductive proof is probably not expected from the students. However, students should be able to be convinced that because the sides of a parallelogram are parallel and equal there should be no overlap of the pieces. This allows students to use the moving and additivity principle to explain why the areas of the two shapes are equal. Further, if students are aware the sum of interior angle measures of a quadrilateral is 360 degrees, it should be easy to convince students why the fourth angle of the rearranged pieces not marked with a right angle symbol is also right.