Question

The formula of which regular shapes can be calculated using the formula base*height

Answer 1

A regular shape means it is equilateral and equiangular.
The formula base * height can then only be applied for a square as that comes closer to a rectangle (which is not a regular shape.

Now if you are looking which polygons (and not specifically regular) this formula can be used, then we can find area using base * height for any parallelogram those would include rectangle, square, rhombus and parallelogram.