Collection of puzzles on 2D polyanimals

For each of the problems below, note that I am using words such as "congruent" and "equilateral," because as teachers, we all know what these mean. However, depending on your students, you might say "same shape and size" instead of congruent, or "triangles having all three sides the same length," instead of "equilateral."

If you cut a square along its two diagonals, you get four triangles congruent isosceles triangles. How many shapes can you make by putting these triangles together? You are only allowed to match edges. That is, you may only fit short sides to short sides, and long sides to long sides.

Source: Four Triangles Puzzle by NRICH

In how many ways can \(n\) congruent equilateral triangles be put together, for small \(n?\)

What if we cut each of those equilateral triangles into thirds?

What if we cut each of those isosceles triangles in half?

Source: Putting Two and Two Together by NRICH

In how many ways can we fit 5 congruent squares together? The answer is 12. Can you find three distinct pentominoes that fill a 3x5 rectangle? 4x5? 5x5? What other size rectangles can be filled with distinct pentominoes, if any? What about fitting \(n\) congruent squares together, for small \(n?\)

See puzzles on convex polygons for puzzle ideas involving convex polyanimals.