SOLUTION: I cant seem to get the right answer to this question, I have tried it numerous times. Cassie is renovating her kitchen countertop. The dimensions of the countertop is 83cm by 20

Question 1062297: I cant seem to get the right answer to this question, I have tried it numerous times.
Cassie is renovating her kitchen countertop. The dimensions of the countertop is 83cm by 203cm. The tiles they will be placing on the counterop are octagonal and square in shape and the pattern will be four octagons surrounding one square. The square tiles are 3cm along one side. Estimate the number of tiles she will need to cover the counterop.
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
If you look at the pattern you get, you realize that
there is the same number of squares and octagons.
Not convinced? Here is how I see it:
Moving along any one side of any square and continuing in that direction you go
by the side of that square, through an octagon,
by the side of another square, through another octagon,
and so on.

We could say that one square plus one octagon is a repeating pattern.
What is the area of that repeating unit?
The area of an octagon of side can be calculated as
,
while the area of a square of side is simply .
The area (in square cm) of one square tile plus one octagonal tile will be
.

The area of the countertop is

.

The number of times the repeating pattern fits into the countertop surface
is a good (under)estimate of the number of tiles of each shape needed.
It can be calculated as
.

Having to cut tiles to make the pattern fit,
quite a few extra tiles will be needed.
The pattern fits 8.1 times along the 83 cm width,
which hopefully could be 8 repeats plus the space between tiles,
but the 203 cm length would take 19.8 repeats,
which will require cutting through the last 8 repeats along the width.
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