[quote]Let T be the triangle with vertices at (4,10), (−8,8),(3,8). The area of T is = ? [quote]

i used the projection forumla and got the length of 1 side as: 4.2426 (not sure if that is right). should i do the same thing to find the other sides?

Printable View

- Jan 15th 2008, 11:04 AMvietvector projection
[quote]Let T be the triangle with vertices at (4,10), (−8,8),(3,8). The area of T is = ? [quote]

i used the projection forumla and got the length of 1 side as: 4.2426 (not sure if that is right). should i do the same thing to find the other sides? - Jan 15th 2008, 11:08 AMtopsquark
[QUOTE=viet;98972][quote]Let T be the triangle with vertices at (4,10), (−8,8),(3,8). The area of T is = ?

Quote:

i used the projection forumla and got the length of 1 side as: 4.2426 (not sure if that is right). should i do the same thing to find the other sides?

-Dan - Jan 15th 2008, 12:11 PMPlato
It is really easy we recall a basic formula:

$\displaystyle A = \frac{1}{2}a \cdot b\sin \left( \phi \right) = \frac{1}{2}\left\| {a \times b} \right\|.$

That is one-half the dot product of the two vectors forming two sides of the triangle times the sine of the angle between. But sine is related to the cross product.