Does a regular decagon tesselate

Answer 1

No. It doesn't tessellate. (You cannot tile out an area with small decagons.)

The sum of the measures of the interior angles of a polygon

with n sides is (n-2)180°

So the sum of all the interior angles in a decagon add up to (8x180)= 1440°.

To find only ONE angle you need to divide 1440 by 10, yielding 144.

360 divided by 144 is 2.5, not an integral number.

This shows that a decagon doesn't tessellate.

In fact, only the regular (equilateral) triangle, the square, and the regular hexagon will tessellate.

For example:

The sum of all the interior angles in a triangle add up to 180. 180 divided by 3 is 60. 360 divided by 60 is 6 (an integral number). This shows that a triangle will tessellate. Try this method with a square (or hexagon) and you will see that it works (square 360/90=4 and hexagon 360/120=3).

Answer 2

No.