It depends what shape the base is:
Triangle: One-half times base times height
Rectangle: Length times width
Parallelogram: Base times height
Circle: Pi times radius squared
Square: Side squared
Other figures' areas are made up of these.
Tetrahedron
pyramid
It could be a pyramid.
Cone
It is simply called a face.
Tetrahedron
Because the base of a cone is round, it is the only three dimensional figure with only one vertex.
pyramid
pyramid or cone
It could be a pyramid.
Cone
It is simply called a face.
It can be a triangular based pyramid
A hemisphere is one example.
Tetrahedron has three sides and a base all triangular.
A hexagonal pyramid.
A pyramid.