Parallelograms

Here's a proof of this :

Let parallleogram ABCD = area ABCD  with a base of 2 and a height of 1

Let areas ABE and DCF  be triangles with equal bases and heights = 1  [ thus, they are equal ]

Now......subtract area ABE from area ABCD   and this gives area EBCD

Add area DCF to this result....so.....

Area EBCD + area DCF  = area EBCF   ......and area EBCF is a rectangle with a base of 2 and a height of 1

So

area EBCD + area DCF  = area EBCF

[area ABCD - area ABE] + areaDCF  = area EBCF

area ABCD + [ areaDCF - area ABE]  = area EBCF

areaABCD + [0]  = areaEBCF

area ABCD   = area EBCF

Thus, parallelogram ABCD with a base of 2 and a height of 1   = the rectangle EBCF  with the same base and height