No. It has a triangular base. If it was a square, it'd be a pyramid.
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If it is a pyramid, then the base shape is a SQURE. If it is a tetrahedron, then the base shape is a triangle.
Yes, a square based pyramid is called a tetrahedron.
Triangle In a tetrahedron, all sides are triangles
A tetrahedron is a triangular based pyramid and its area is worked out as for a triangle that is 0.5*base*height.