i know the regular cross product gives the area of parallelogram, but how do i find the area of trapezoid?

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- May 2nd 2009, 09:22 AMMottoV2How do i find area of trapezoid using vector cross product?
**i know the regular cross product gives the area of parallelogram, but how do i find the area of trapezoid?** - May 2nd 2009, 09:35 AMPlato
You can partition

**any trapezoid into two triangles.**

The area of any triangle is one-half the corresponding parallelogram:

$\displaystyle \frac{{\left\| {\overrightarrow a \times \overrightarrow b } \right\|}}

{2}$, where $\displaystyle \overrightarrow a \;\& \,\overrightarrow b $ are adjacent sides. - May 2nd 2009, 09:55 AMMottoV2
so that means the area of trapezoid is same as the area of parallelogram?

edit: oh wait, are they divided into identical triangles?

edit again: k i got it :-D. thx - May 2nd 2009, 10:15 AMPinkk
They don't have to necessarily be equal.

- May 2nd 2009, 10:15 AMPlato