The cover of a soccer ball consists of interlocking regular pentagons and regular hexagons. Why can't they be interlocked in this pattern to tile a floor?

Because of gaps between the vertex of Pentagons and hexagon.

Step-by-step explanation:

The Pentagon has 5 sides and 5 vertex angles. While hexagon has 6 sides and six vertex angles

The sum of the angle of polygon is equal to ( n - 2 )180

Sum of the angle of a Pentagon will be: (5 - 2)×180 = 540

Each vertex angle of a Pentagon = 540/5 = 108

Sum of the angle of hexagon will be: (6 - 2)×180 = 720

Each vertex angle of a hexagon =

720/6 = 120

To interlock Pentagon and hexagon, the sum of the combination of vertex angles of both must be equal to 360 ( sum of the angles at a point = 360)

Since there is no number of combinations that can be equal to 360, there will surely be a gap.

18

step-by-step explanation:

draw the shape and you will see that f and k are actually at adjacent vertices (points of the hexagon that are neighboring).   so find the distance between (1,2) and (4,2).   that is easy since (1,2) and (4,2) is just a vertical distance to count, which is 3.   it is a regular polygon which means all sides are congruent.   you have 6 sides (hexa) so multiply 6 by 3 to receive 18.

hello i am doing good for you that it's summer in your country or state ; )

btw in my country we just have sun and rain as (because i live in the caribbean lol)

also, thx a lot for the points : )