# parallelogram area help

• November 21st 2013, 03:52 PM
Tweety
parallelogram area help
Find the area of the parallelogram with vertices at (1,4), (2,-5), (5,-2) and (4,7)

I know the formula is ad-bc

however how do i work out what the vectors (a,b) and (c,d) are?

its suppose to be (3,3) and (1,-9)

I have drawn a diagram, but it still does not help, what are the non-parallel edges?
• November 21st 2013, 04:07 PM
chiro
Re: parallelogram area help
Hey Tweety.

Did you plot the figure geometrically? Also remember to break things up into triangles and add the areas.

Hint: The length of the vector |axb| gives the area of the triangle that is enclosed within the vectors a and b.
• November 21st 2013, 04:43 PM
HallsofIvy
Re: parallelogram area help
No, chiro. |a x b| gives the area of the parallelogram having vectors a and b as two sides. The area of the triangle is (1/2)|a x b|.
• November 21st 2013, 04:52 PM
chiro
Re: parallelogram area help
Yes you are spot on: thanks for picking that up! (1/2absin(C) = 1/2 |axb|).
• November 21st 2013, 04:59 PM
Plato
Re: parallelogram area help
Quote:

Originally Posted by Tweety
Find the area of the parallelogram with vertices at (1,4), (2,-5), (5,-2) and (4,7)
I know the formula is ad-bc
however how do i work out what the vectors (a,b) and (c,d) are?
its suppose to be (3,3) and (1,-9)
I have drawn a diagram, but it still does not help, what are the non-parallel edges?

@Tweety, I am constantly amazed how little you seem to know about questions that you are asked to solve.
If you have not been taught this theorem then your course is a SHAM

Theorem: If $\vec{A}~\&~\vec{B}$ are adjacent sides of a parallelogram then
$\|\vec{A}\times\vec{B}\|$ is the area of that parallelogram.
• November 22nd 2013, 02:10 AM
Tweety
Re: parallelogram area help
errmm well I know this formula, but my problem was I did not know 'how to apply it, and also I missed classes when this was being taught so i am just reading it off a text book......
• November 22nd 2013, 10:10 AM
emakarov
Re: parallelogram area help
To find the coordinates of a vector, subtract the coordinates of the beginning from those of the end.

This follows from the definition of coordinates and operations of vectors. In my course, the coordinates of a point are by definition the coordinates of the radius-vector to that point. That is, if O is the origin, the coordinates of a point A are the coordinates of the vector OA. Now, a vector AB equals OB - OA, so the coordinates of AB are the coordinates of B minus the coordinates of A.