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### Tiling a Floor

```
Date: 06/30/99 at 18:23:02
From: Melissa
Subject: Math conversion of yards and feet

If you have a 12 ft. x 15 ft. square room, how many square yards is
it? Is it 20? Also, for a 30 square foot room how many 8" x 8" tiles
would you need?

Thank you so much.
```

```
Date: 07/01/99 at 08:38:36
From: Doctor Rick
Subject: Re: Math conversion of yards and feet

Hi, Melissa.

You are correct about square yards. First convert the linear
dimensions from feet to yards: 12 ft = 4 yd, 15 ft = 5 yd. Then when
you multiply yards by yards, you get an area in square yards, namely,
4 yd * 5 yd = 20 square yards.

Tiling is trickier because tiles around the edges will probably need
to be cut, and this will require that you buy extra tiles. The first
approximation, ignoring this complication, works like this:

1 square foot = 12 inches * 12 inches  = 144 square inches

30 square feet = 30 * 144 square inches = 4320 square inches

1 tile = 8 inches * 8 inches = 64 square inches

4320 square inches / 64 square inches = 67.5 tiles

Now for the complication. Let's suppose the room is 5 feet by 6 feet,
or 60 inches by 72 inches. Divide each length by the width of a tile
to find out how many tiles will fit across that direction:

60 inches / 8 inches = 7.5 tiles
72 inches / 8 inches = 9 tiles

In an ideal situation, you could have 9 tiles by 7 tiles = 63 tiles,
plus a row of 9 half-tiles (made from 4 1/2 whole tiles) along one
side, totaling 67 1/2 tiles, the same as I got before.

But having tiled some bathrooms, I know that the room is probably not
quite rectangular. The standard way to tile a floor is to start from
the center and arrange it so you have at least a half tile all around.
Having cut tiles along all the walls allows you to compensate for
irregularities, and everything looks symmetrical. In my hypothetical
case, I would center a rectangle of 6 by 8 tiles, leaving 1.5 / 2  =
3/4 tile on either side in the short direction, and 1/2 tile on either
side in the long direction.

|                                   |
|<----- 9 tiles = 1/2 + 8 + 1/2---->|

+-+---+---+---+---+---+---+---+---+-+  ---
+-+---+---+---+---+---+---+---+---+-+   ^
| |   |   |   |   |   |   |   |   | |   |
+-+---+---+---+---+---+---+---+---+-+   |
| |   |   |   |   |   |   |   |   | |   |
+-+---+---+---+---+---+---+---+---+-+   |
| |   |   |   |   |   |   |   |   | |   |
+-+---+---+---+---+---+---+---+---+-+  7.5 tiles = 3/4 + 6 + 3/4
| |   |   |   |   |   |   |   |   | |   |
+-+---+---+---+---+---+---+---+---+-+   |
| |   |   |   |   |   |   |   |   | |   |
+-+---+---+---+---+---+---+---+---+-+   |
| |   |   |   |   |   |   |   |   | |   |
+-+---+---+---+---+---+---+---+---+-+   v
+-+---+---+---+---+---+---+---+---+-+  ---

6 * 8 = 48 whole tiles
2 * 8 = 16 tiles cut to 3/4
2 * 6 = 12 tiles cut to 1/2
4 corner tiles cut to 3/4 by 1/2
--
80 tiles total

You might get away with fewer tiles than this (by using both halves of
the half-tiles), but I would buy the full 80 tiles to be on the safe
side.

Home repair books give a formula to figure all this out; I don't have

- Doctor Rick, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Euclidean/Plane Geometry
High School Geometry
High School Practical Geometry
High School Symmetry/Tessellations
High School Triangles and Other Polygons
Middle School Geometry
Middle School Triangles and Other Polygons
Middle School Two-Dimensional Geometry

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