Area of Parallelograms
This lesson presents the idea that the area of any right triangle is exactly half of a certain rectangle, and contains varied exercises for students. To find the area of any right triangle, you simply multiply the lengths of the two sides that are perpendicular to each other, and then take half of that.




The area of a parallelogram is the same as the area of the corresponding rectangle. 
1. Imagine moving the marked triangle to the other side as shown. What is the area of the original parallelogram?
2. Draw a line in each parallelogram to form a right triangle. Imagine moving that triangle to the
other side so that
you get a rectangle, like in the examples above. Find the area of the rectangle,
thereby finding the area of the
original parallelogram.
a. _________ sq. units
b. _________ sq. units c. _________ sq. units d. _________ sq. units 

3. Draw an altitude to each parallelogram. Highlight or “thicken” the base. Then find the areas.
a. _________ sq. units
b. _________ sq. units c. _________ sq. units d. _________ sq. units e. _________ sq. units 
4. a. Draw the
altitudes to the parallelograms and mark their bases. One parallelogram's
altitude is already
marked. Notice how that altitude does not “reach” the base, but instead ends
at the continuation of
the base. That is no problem—what matters is that
the altitude is perpendicular to the base.
b. Find the areas of these parallelograms. What do you notice?
5. Draw as many differently shaped parallelograms as you can that all have an area of 12 square units.
8. Find the area of the parallelogram in square meters.
This lesson is taken from Maria Miller's book Math Mammoth Geometry 2, and posted at www.HomeschoolMath.net with permission from the author. Copyright © Maria Miller.
Math Mammoth Geometry 2
A selfteaching worktext for 6th and 7th grades that covers the area of triangles, parallelograms, and polygons, pi, area of circle, nets, surface area, and volume of common solids.
Download ($5.70). Also available as a printed copy.