# How do i find area of trapezoid using vector cross product?

• May 2nd 2009, 10:22 AM
MottoV2
How 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, 10:35 AM
Plato
Quote:

Originally Posted by MottoV2
i know the regular cross product gives the area of parallelogram, but how do i find the area of trapezoid?

You can partition any trapezoid into two triangles.
The area of any triangle is one-half the corresponding parallelogram:
$\frac{{\left\| {\overrightarrow a \times \overrightarrow b } \right\|}}
{2}$
, where $\overrightarrow a \;\& \,\overrightarrow b$ are adjacent sides.
• May 2nd 2009, 10:55 AM
MottoV2
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, 11:15 AM
Pinkk
They don't have to necessarily be equal.
• May 2nd 2009, 11:15 AM
Plato
Quote:

Originally Posted by MottoV2
so that means the area of trapezoid is same as the area of parallelogram? edit: oh wait, are they divided into identical triangles?

No. There are most likely two different triangles.
Find the area of each and add together.