Answer:
25 tiles
Step-by-step explanation:
There are a couple of ways to work a problem like this. Here, they pretty much amount to the same thing.
- Figure the area of the room and divide that by the area of one tile to find the number of tiles.
- Figure the dimensions of the room in terms of tile dimensions, then multiply those values to find the number of tiles needed.
In either case, you need to consider how partial tiles are handled. Here, the room dimensions are 4.5 feet and 5.5 feet, and the tile dimensions are 1 ft by 1 ft. So, the room is 4.5 tiles by 5.5 tiles. Since the leftover is exactly 1/2 tile, we can assume that a tile can be cut in half and the two parts used in two places where half-tiles are needed.
If the room were a little larger, say 4 ft 7 inches, then 5 inches of tile would be left after cutting to fit the 7-inch space. Two of those 5-inch leftovers could be cut to fit another 7-inch space, but the installation starts to have a messy appearance--especially if the tiles have a pattern. In this example, you might want to say the room dimension is 5 tiles, and the extra 5 inches will be wasted.
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The area of the floor is the product of its dimensions ...
(5 + 1/2)(4 + 1/2) = 5·4 + 5·1/2 +4·1/2 + 1/2·1/2
= 20 + 9·1/2 + 1/4 . . . . . 20 whole tiles + 9 half-tiles + 1 quarter-tile
= 20 + 4 1/2 + 1/4
= 20 + 4 3/4
The contractor will need 20 whole tiles and 5 tiles cut in half. One of those half-tiles will need to be cut in half again. Altogether, 25 whole tiles are needed if the cuts can be made so that both halves are usable.
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The other method has you figure the area of the room ...
(4.5 ft)(5.5 ft) = 24.75 ft²
and divide that by the area of 1 tile to find the number of tiles:
(24.75 ft²)/(1 ft²/tile) = 24.75 tiles
If we're buying whole tiles, we need 25 of them.
