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May 2013

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The ideas in this geometry lesson are taken from Math Mammoth Geometry 1 book.

Area of parallelogram
Free geometry lesson plan from HomeschoolMath.net

Look how we can cut a piece from a parallelogram and "glue" it to the other end and thus make a rectangle: Here is the parallelogram. We draw an ALTITUDE to the parallelogram ( = a line from one vertex down to the base so that it is perpendicular to the base).   Thus is formed a right triangle.  We move that triangle as shown. And now we have a rectangle! What is its area? The area of the final rectangle is the SAME as the area of the original parallelogram. Can you see why?

The one side (the horizontal side in the picture) of the final rectangle is the same as the side of the parallelogram. The other side of the rectangle (the vertical side) is the altitude of the parallelogram. Therefore, the area of a parallelogram is SIDE ALTITUDE.

Look at other examples: Here is the parallelogram. We draw the altitude and move the right triangle as shown. Now we have a rectangle! What is its area? This parallelogram is the other way, so we draw the altitude  in the horizontal direction. You can turn your head to view this as usual.  Still the altitude is perpendicular to the one side of the parallelogram. Again we have a rectangle! What is its area?

Example problem types

1.  Find out the area of the following parallelograms.

2.  Here you see two different shaped parallelograms that have the area of 15: On a grid paper, in each case draw 4 different parallelograms that have the area of a)  20     b)  8    c)  12

Next geometry lesson