There are an infinite number of shapes, because a shape can have any number of sides. This is where we get into our laws of fractals. A fractal is a shape with an infinite perimeter and area, meaning that every level of infinity is another shape, but can be beat by another shape. However, this is all philosophical math and goes way beyond the context of your question.
To keep it short and simple, there are an infinite number of shapes in the world.
