How to you draw 2 different parallelograms that each have an area of 4 square inches? It can't be a rectangle or a square.
Start with a row of 4 1 inch x 1 inch squares in a row. That's
4 square inches, like this:
But that won't do. So let's draw the diagonal of the left square,
like the green line below:
Now draw another green line parallel to it on the far right side,
like this:
Draw a line from the top of that green line on the right
over to the last square on the right, like this.
That rectangle we've added on the right is exactly like the triangle on
the far left. So let's erase the triangle on the far left, like this:
That's a parallelogram which is 4 square inches in area.
The triangle we erased off the far left side is the same amount of
area as the triangle we put on on the far right. If you like you
can erase the partitions and just show the parallelogram:
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Now start with 4 1 inch by 1 inch squares arranged like this:
Now do the same sort of thing. Draw these two parallel
green lines, and a line from the top of the right green line
leftward to the squares:
Erase the triangle on the far left, which has the same area
as the triangle we've added on the far right, so the resulting
parallelogram has 4 square inches of area. I'll erase the
"partitions" too:
There you go!
Edwin
