Question

Explain why not all regular polygons will tessellate.

Answer 1

which grade is it?

Answer 2

true

Answer 3

Since the regular polygons in a tessellation must fill the plane at each vertex, the interior angle must be an exact divisor of 360 degrees. This works for the triangle, square, and hexagon, and you can show working tessellations for these figures. For all the others, the interior angles are not exact divisors of 360 degrees, and therefore those figures cannot tile the plane.

Answer 4

They don't all have interior angles that are factors of 360 degree? @d3Xter

Answer 5

A regular polygon will tessellate (the plane) if and only if the measure of an interior angle evenly divides 360 or equivalently (n - 2) | 2n. And if (n - 2) | 2n, then (n - 2) must also divide (2n) - 2*(n - 2) which equals 4. Therefore, n = 3, 4, or 6. We see that only an equilateral triangle (n = 3), a square (n = 4), or a regular hexagon (n = 6) will tessellate. All other regular polygons will not.

Answer 6

does that help

Answer 7

Yes, @parisgirl1515. The rest aren't exact divisors... :)

Answer 8

do i get a medal....lol

Answer 9

sure