# area of parallelogram

• Sep 6th 2008, 12:13 PM
Allie
area of parallelogram
Find the area of the parallelogram with vertices (5,1), (8, 6), (12, 9), and (15, 14)
How would I start this problem?
• Sep 6th 2008, 12:17 PM
skeeter
have a look how it's done ...

Area of Parallelogram from Vector Cross Product
• Sep 6th 2008, 12:36 PM
Allie
thank you that is very useful but i must be doing something wrong in my calculations the vector i get from those points are 3i+5j+0k for both, when i take the cross product the answer is 0. I know that is not correct. What's wrong with my calculations
• Sep 6th 2008, 01:27 PM
ILoveMaths07
Allie, a sketch always helps. What you're doing is... You're finding the vector of a diagonal of the parallelogram BC instead of the adjacent side, AC. Calculate the vector product $\vec{AB}\times\vec{AC}$.

I hope that helps. :)

ILoveMaths07.
• Sep 6th 2008, 02:05 PM
Allie
haha the sketch does not help i don't even see parallelogram in the sketch, it looks like a straight line
• Sep 6th 2008, 02:11 PM
skeeter
not a line, but a very "skinny" parallelogram

(5,1) to (8,6) and (5,1) to (12,9)

first side vector ... u = 3i + 5j

adjacent side vector ... v = 7i + 8j

now find the cross product.
• Sep 6th 2008, 02:22 PM
Allie
ok i got it now thank you

Now would i do the same for this problem?
Find the volume of the parallelepiped defined by the vectors

(5,2,1) (-3,-2,5) (2,5,-2)
• Sep 6th 2008, 02:32 PM
skeeter
• Sep 6th 2008, 02:50 PM
Allie
thank you that website is very helpful