Calculate 3D Triangle Area with Coordinates: Formula & Example

To calculate the area of a 3D triangle given its coordinates, you can use the following formula:

Area = 1/2 * | AB x AC |

where AB and AC are the vectors formed by subtracting the coordinates of point A from points B and C, respectively, and x represents the cross product operator.

Here's an example:

Suppose we have a triangle with the following coordinates:

A = (1, 2, 3) B = (4, 5, 6) C = (7, 8, 9)

To find the area, we first need to calculate AB and AC:

AB = (4-1, 5-2, 6-3) = (3, 3, 3) AC = (7-1, 8-2, 9-3) = (6, 6, 6)

Next, we take the cross product of AB and AC:

AB x AC = (3, 3, 3) x (6, 6, 6) = (-18, 0, 18)

The magnitude of the cross product is:

| AB x AC | = sqrt((-18)^2 + 0^2 + 18^2) = 3sqrt(12)

Finally, we plug this value into the area formula:

Area = 1/2 * 3sqrt(12) = 3sqrt(3)

Therefore, the area of the triangle with coordinates A, B, and C is 3sqrt(3).