How do you find the area of a parallelogram with 4 given vertices? Such as A(-1, 3) B(0, 6) C(5, 5) D(4,2)?

Question

How do you find the area of a parallelogram with 4 given vertices? Such as A(-1, 3) B(0, 6) C(5, 5) D(4,2)?

Answer 1

Here are two ways: see this figure http://i33.tinypic.com/27zgms4.jpg

Compute the area of the rectangle defined by

(-1,2) (-1, 6) (5,6) (5,2) which is 24  (red outline)

Then subtract the 4 right triangles (light blue)

which are outside the parallelogram.

which add up to 1x3 and 1x5 (half of each, twice)

Result: 24 - 8 = 16.

Another way is to start with the central rectangle (dark blue)

bounded by (0,3) (0,5) (4,5) (4,3) which has area 8.

And add the 4 right triangles which surround it: (red and white)

1x3 and 1x5 again (half of each twice).  Total 16.

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