Calculating the Area of a Parallelogram Using Diagonals: A Vector Approach

[Angello90]

Homework Statement

Find the area of the parallelogram with diagonals a = 3i + j − 2k and b = i − 3j + 4k


The attempt at a solution

I know that |x| X |y| will give the area, but will it hold for diagonals? Or do I have to find x and y vectors?

 

[HallsofIvy]

No, you can't just take the cross product of the diagonals. But if you draw two identical parallelograms side by side, you should be able to see that the sum of the two diagonals is twice the base vector. And putting one on top of the other, that the difference is twice the side vector.

 

[Angello90]

Ok so basically, |((A+B)/2) X ((A-B)/2)| = Area; where (A+B)/2 is a base and (A-B)/2 is a side?

Thanks a mil HallosofIvy!