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 = [tex]\frac{3\sqrt{3}}{2}[/tex][tex]a^{2}[/tex]
Where a is the length of side.
Therefore:
A = [tex]\frac{3\sqrt{3}}{2}[/tex][tex]20^{2}[/tex]
A = [tex]\frac{3\sqrt{3}}{2}[/tex] X 400
A = (400 x 3 x [tex]\sqrt{3}[/tex]) / 2
A = [tex]\frac{2078.460969}{2}[/tex]
A = 1039.23[tex]cm^{2}[/tex]
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[tex]cm^{2}[/tex]
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
