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.
A figure without bent lines inspired by Woody3's first figure (and by my notebook).