They can, so the question is totally misguided.
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A regular octagon will not tessellate but an irregular one will.
Square, yes. Triangle, no.
no it cant be...
A triangle can't be a square. A triangle only has 3 points, squares have 4.
If an equilateral triangle and a square have equal perimeters, then the ratio of the area of the triangle to the area of the square is 1:3.