Question

Hexagonal tiles of side 20 cm are used to tile a room which measures 6.25 m by 4.85 m. Assuming we complete the edges by cutting up tiles, how many tiles are needed?

Answer 1

Answer: 292 tiles

Explanation:

To find the number of tiles needed , we need to know the area of the hexagonal tiles and also the area of the room.

Area of hexagon

The area of hexagon is given as :

Area =
`(3√(3))/(2)`
`a^(2)`

Where a is the length of side.

Therefore:

A =
`(3√(3))/(2)`
`20^(2)`

A =
`(3√(3))/(2)` X 400

A = (400 x 3 x
`√(3)`) / 2

A =
`(2078.460969)/(2)`

A = 1039.23
`cm^(2)`

Also to find the area of the room , we must first convert from m to cm

6.25 m = 6.25 x 100 cm

6.25m = 625 cm

4.85m = 485cm

Therefore: Area of the room = length x breadth

Area = 625 x 485

Area = 303125
`cm^(2)`

Therefore , the number of tiles needed = area of the room / area of hexagon

Number of tiles = 303125/ 1039.23

N = 291.6823032

Therefore , the number of tiles needed ≈ 292