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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
     +-+---+---+---+---+---+---+---+---+-+  ---

This adds up to

     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 
access to mine right now. I hope this helps a little.

- 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
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Middle School Triangles and Other Polygons
Middle School Two-Dimensional Geometry

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