Question

Mark is installing a mosaic tile backsplash and the shape of the tiles are shaped like regular hexagons. Each tile has a radius of 2in and he needs to cover a rectangular area that measures 132 in by 18 in. Each piece of tile costs 3.49 to buy. How much will the tile cost Mark to purchase?

Answer 1

tile will cost
`\$806.6` Mark to purchase .

Explanation:

Here we have , Mark is installing a mosaic tile backsplash and the shape of the tiles are shaped like regular hexagons. Each tile has a radius of 2 in and he needs to cover a rectangular area that measures 132 in by 18 in. Each piece of tile costs 3.49 to buy. We need to find How much will the tile cost Mark to purchase . Let's find out:

We know that area of hexagon is given by :

⇒
`(3√(3) s^2)/(2)`

According to question , s=2 inch

⇒
`(3√(3) (2^2))/(2)`

⇒
`6√(3)`

⇒
`10.38in^2`

Now , area of rectangular area :

⇒
`length(width)`

⇒
`132(18) in^2`

Now , Number of tiles required is : (Area of rectangle )( Area of hexagon )

⇒
`(132(18))/(10.38)`

It's given that , one tile cost 3.49 , So
`(132(18))/(10.38)` will cost :

⇒
`(132(18))/(10.38)(3.49)`

⇒
`\$806.6`

Therefore , tile will cost
`\$806.6` Mark to purchase .