It is possible to tessellate a plane with squares, triangles, and hexagons. To tessellate something means to cover it with repeated use of a single shape, without gaps or overlapping.
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no * * * * * Actually, the answer is YES.
Yes. See: http://euler.slu.edu/escher/index.php/Tessellations_by_Polygons#Tessellations_by_Quadrilaterals
yes... this figure does tessellate
No it does not tessellate you have to pentagons in order for it to tessellate. * * * * * It is not at all clear what "have to pentagons" has to do with this. No polygon with 7 or more sides will tessellate. Octagons will tessellate if mixed with squares but that is not "proper" tessellation since it involved more than one shape.
A regular pentagon will not tessellate.