There are five of them. One at each corner of the rectangular base, and the fifth at the apex where the triangular faces meet.
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5.
A rectangular based pyramid has 5 faces, 8 edges and 5 vertices whch is the plural of vertex.
A rectangular prism has 6 vertices. A rectangular pyramid has 5 vertices. 6-5= 1 more vertex
There are many such solids: A heptagonal pyramid A cuboid (or rectangular prism) A hexagonal dipyramid A pentagonal pyramid with a 2-vertex shape on the other side etc.
They are both solids with a four vertex base.