To find the area you would use the same equation for a normal triangle which is 1/2 x base x height
1/2 x b x h
base x height x 1/2
To calculate the area of a 3 dimensional triangle you can use the formula (1/2 * b* h)
Please note that all triangles are 2-dimensional figures. There can be 3-dimensional triangles. Thus there is no question of finding area of a three dimensional triangle.
However we do have 3-dimensional solids, that have triangle shaped faces. For example, a solid called tetrahedron having four vertexes (extreme points) has four triangular faces. A Triangular prism has two triangular faces and three rectangular faces. A square pyramid has a square base and four triangular sides.
We can find areas of triangular or other shaped surfaces of such solids by working out areas of each face separately and then adding them together.
The plane figure enclosed by 3 intersecting straight lines is a triangle. Or any 3 points non collinear (not forming a straight line) is always in a plane. The are of the triangle is (1/2) of a side times the height of the opposite vertex from the base.
In 3 dimensional space also the triangle has its 3 vertices in one single plane. Or in other words any 3 non collinear points in space form a plane triangle. So the formula to calculate the area of the triangle in 3 dimension is the same: (1/2)base*height.