One square into 3 equal squares
Dissect a square into 3 equal squares. Solution
Bonus : into 3 squares of areas in ratio 2:3:4
A rotated square
Dissect a square in just 5 pieces to make the same square, rotated by 45°, but without rotating nor flipping the parts, just translations are allowed.
Details (rectangle to square and square to several squares, or turned).
A triangle into a square
Dissect an equilateral triangle in 4 pieces to build a square. Solution
Details (triangle to square).
Bonus : Any triangle into a square, a triangle into another triangle.
An hexagon into a triangle
Dissect a regular hexagon in just 5 pieces to build an equilateral triangle. Solution
A pentagon into a square
Dissect a regular pentagon in 6 pieces to build a square Solution
Crosses and stars
Dissect a greek cross or a latin cross into a square.
Dissect an hexagram (star hexagon) into a square.
Details (crosses and stars).
Bonus : other crosses, n-gon and n-gram cross-dissections.
Details (misc. shapes).
Of course not squaring the circle !
But dissect into a square :
The crescent is made of two equal circle arcs.
(hence connected by a straight segment !)
The urn is made of circle arcs with same radius.
Details (curved shapes).
Bonus : crescent to greek cross, curved shapes to curved shapes.
For instance the classical round table into two oval tables.
... in 6 parts only !
And the dissection of a flower into a circle.
(the hardest part is to find the exact shape of the flower, so the dissection is possible...)