Hexagonal tiles of sides20cm are used to tile a room which measures 6.25m. Assuming we complete the edges by cutting up tiles, how many tiles are needed?
You need to provide more than one linear dimension for the room. Is the room square or rectangular? Is the 6.25 m number supposed to be SQUARE meters? If so, you should so designate.
Its rectangular room of 6.25m by 4.85m
The distance between opposite sides of the hexagons will be 20sqrt3 = 34.64 cm.
If hexagon edges are parallel to the long wall, you need 4.85/0.3464 = 14 tiles along the short wall. Along the long wall, adjacent pairs take up 0.60 m, so you need 6.25/0.60 = 10.42 pairs or 21 staggered rows. Ten of those rows will require half-hexagons at the ends, but you can use both halves of a cut one.
I claim the answer is 21x14 = 294 tiles. See what you get.
If you just divided the area of the room by the area of each tile, you would get 292, but that would assume no pieces wasted. I would order 300 times to be safe.
To find out how many tiles are needed, we need to calculate the area of the room and the area covered by one tile.
First, let's convert the side length of the tiles from centimeters to meters. 20cm is equal to 0.2m (since 1 meter is equal to 100 centimeters).
Now, let's calculate the area of the room:
Length of the room = 6.25m
Width of the room = 6.25m (assuming the room is square)
Area of the room = Length × Width = 6.25m × 6.25m = 39.06 square meters
Next, let's calculate the area covered by one tile:
Area of a hexagonal tile = (3√3 × (side)^2) / 2
Where the side is 0.2m.
Using the formula:
Area of one tile = (3√3 × (0.2m)^2) / 2
= (3.8971 × 0.04) / 2
= 0.15588 square meters
Now, we can determine the number of tiles needed by dividing the area of the room by the area of one tile:
Number of tiles = Area of the room / Area of one tile
= 39.06 square meters / 0.15588 square meters
≈ 250 tiles
Therefore, approximately 250 tiles are needed to tile the room.