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All quadrilaterals are 4 sided shapes
There can be no formula for a tetrahedron since you have not specified what aspect the formula is supposed to calculate. Furthermore, although they are all triangular pyramids, tetrahedra can be tall, needle-like shapes or almost flat shapes.
There is no formula as such. You partition the compound shape into simpler shapes whose areas you can work out using formulae, and then add all those parts together.
There is no general formula to "work out" a rhombus. It all depends on the information that you have and the information that you require.
Yes. Heron's Formula works on all triangles.