Assuming my last comment on the question, then the answer is
This is due to Wallace-Bolyai-Gerwien Theorem: "Two polygons are congruent by dissection iff they have the same area. In particular, any polygon is congruent by dissection to a square of the same area".
For the bonus, the best known dissections are
due to Theobald, G. "Geometric Dissections."
For the original question (before the circle was removed),
"Laczkovich (1988) also proved that a circle is congruent by dissection to a square (furthermore, the dissection can be accomplished using translations only)."
~ "Weisstein, Eric W. "Wallace-Bolyai-Gerwien Theorem." From MathWorld--A Wolfram Web Resource."
~ "Laczkovich, M. "Von Neumann's Paradox with Translation." Fund. Math. 131, 1-12, 1988."