A triangular based pyramid seems to fit the description which has 4 faces, 6 edges and 4 vertices
A pyramid.
Tetrahedron
There is a contradiction in your question. If the base has four equal sides then is it a square so not all the faces are Triangles. However if the base is a square and the rest of the faces are triangles then your object is a "Square-based Pyramid"
Triangular prisim. The three faces are rectangles, while the two bases are triangles.
Octogon
The solid figure that has 4 flat surfaces that are triangles is a tetrahedron. A tetrahedron is a polyhedron with four triangular faces, six straight edges, and four vertex corners. Each of the four faces of a tetrahedron is an equilateral triangle, making it a regular polyhedron.
a pyramid, in the sense that most people think of has a square base, with 4 triangle 'sides', which would be 5 faces. A regular tetrahedron has 4 equilateral triangles as faces.
Isosceles TetrahedronA solid with four faces is a tetrahedron. Each of the faces is a triangle. If all the triangles are congruent, you have an isosceles tetrahedron.
Pyramid.
A pyramid.
a pyramid
The answer is a pyramid.
None it is impossible.
A pyramid.
The figure is a pyramid and the base is a square.
triangle based pyramids
pyramid