In a right pyramid the apex is directly above the centroid of the base - whatever shape that is. One consequence is each of the faces, other than the base, are isosceles (or equilateral) triangles.
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It does not have to have any. If it is a right pyramid, it will have 2 pairs.
The answer will depend on the area of the base, whether or not it is a right pyramid, and its height.
The longer of the sides forming the rectangular base of the pyramid.
No but a right angle triangle does
A trapezium or a triangle. If the pyramid is a right pyramid then they would both be isosceles.