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Q: Why can't you use regular pentagons to tile an area?

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Not with regular pentagons because each interior angle is 108 degrees which is not a factor of 360 degrees

No, not if your floor is flat. Regular pentagons do not tile the plane. You will always end up with empty space. You would need to use some other shapes too (or irregular pentagons) http://www2.spsu.edu/math/tile/defs/pentagon.htm

Well, pentagons that tile a plane need to have angles and side lengths that have one or more in the shape.

Yes it can tile. * * * * * No, they cannot.

Find the area of the tile and this will depend on the shape of the tile. Tiles for regular or semi-regular tessellation may be triangular, quadrilateral (square, rectangular, rhombic, parallelograms, trapeziums), hexagonal or octagonal. The formula for the area in each case, is likely to be different.

no

No.

An [equilateral] triangle, square and hexagon are the only regular polygons which, by themselves, will tile a surface.

Yes.

Not regular heptagons.

Yes.

No.

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