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.