Is there a determinant triangle area formula that works in 3D?

We know that for a triangle in 2d, area =
| 0.5 0.5 0.5 |
| x_1 x_2 x_3 |
| y_1 y_2 y_3 |
Is there a similar formula for triangles in space, with points given as (x,y,z) coordinates?

The 2d determinant formula generalizes in 3d to a determinant formula for the volume of a tetrahedron. I do not know one for area of a triangle whose vertices are in (x,y,z) coordinates. But possibly someone else knows of something.

This entry was posted on Wednesday, May 19th, 2010 at 10:55 am and is filed under area formula. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.

One Response to “Is there a determinant triangle area formula that works in 3D?”

Rita the dog on May 19th, 2010 at 4:33 pm

The 2d determinant formula generalizes in 3d to a determinant formula for the volume of a tetrahedron. I do not know one for area of a triangle whose vertices are in (x,y,z) coordinates. But possibly someone else knows of something.
References :

Area List