Paul laid tile on the shaded area of his den. How many square tiles did he use? Den 20 by 14 with 4by 4 tiles

Question

Area is 20 by 14 with 4by4 square tiles to be laid. How many square tiles were used?

Answer 1

More information is needing to solve this problem.  Assuming the den is 20 ft by 14 ft and the the tiles are 4 inches by 4 inches we convert feet to inches.

 

20 ft = 20(12) = 240 inches and 14(12) = 168 inches so the den is 240 inches by 168 inches

 

Note that 4 goes into 240 and 168 evenly,  240/4 =60 and 168/4 = 42.  This means that we need 60 tiles to cover the length of the den and 42 tiles to cover the width of the den.  To cover the entire den we need 60(42) = 2520 tiles.  We can also solve this problem by dividing the total are of the den in inches by the area that one tile covers.

 

number of tiles = (240)(168)/(4*4) = 2520 tiles.

Answer 2

The area of the den is equal to the length times the width: A_Den=L*W=20*14=280

The area of each tile is also equal to its length times width: A_tile=L*W=4*4=16

 

The number of tiles, assuming that you can cut a tile in half, is going to be equal to the area of the den (A_Den) divided by the area of the tile (A_tile). Tiles=A_Den/A_tile=280/16=17.5, but we would need a full 18 tiles in order to get that 17.5 tiles.

 

Another way of looking at the problem is how many tiles you can fit in each row and column. If each row of he den is 20 long, we would be able to fit 5 tiles in each row because the length of each tile is 4 (20/4=5).

If we look at each column, we have 14 long, so we can only fit 3.5 tiles in each column (14/4=3.5).

We then take the number of tiles in each row (5) times the number of tiles in each column (3.5) and get the same answer as before: 5*3.5=17.5.