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

Step-by-step 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 = $\frac{3\sqrt{3}}{2}$$a^{2}$

Where a is the length of side.

Therefore:

A = $\frac{3\sqrt{3}}{2}$$20^{2}$

A = $\frac{3\sqrt{3}}{2}$ X 400

A = (400 x 3 x $\sqrt{3}$) / 2

A = $\frac{2078.460969}{2}$

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