A circle or a rectangle can be easily cut into any number of parts

that are equal by both shape and area. Is there a plane figure with the same

property that has neither a center of symmetry nor a line of symmetry?

The parts must be equal in both shape and area.

My thoughts are the following.

There are not too many figures with this property – some trapezoids (I was checking the right ones) and scalene triangles (I was checking the right ones too). No luck.

Then I got an idea that there can be some combination of a semicircle and a rectangle or a triangle. I checked these figures too – no luck.

## Best Answer

This is trivially achieved by "extruded" shapes.