The first geometric shape that comes to mind with no perpendicular sides is a triangle.
I suppose. All of a square's sides are perpendicular.
A square or a rectangle has perpendicular sides that meet each other at right angles which is 90 degrees.
The question contradicts itself. A dodecagon need not have any perpendicular sides.
There are infinitely many possible answers. For example, any regular polygon with an even number of sides.
shape no pairs of perpendicular sides
It could be a right angle triangle