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 .

Step-by-step 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 :

⇒ $\frac{3\sqrt{3} s^2}{2}$

According to question , s=2 inch

⇒ $\frac{3\sqrt{3} (2^2)}{2}$

⇒ $6\sqrt{3}$

⇒ $10.38in^2$

Now , area of rectangular area :

⇒ $length(width)$

⇒ $132(18) in^2$

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

⇒ $\frac{132(18)}{10.38}$

It's given that , one tile cost 3.49 , So  $\frac{132(18)}{10.38}$ will cost :

⇒ $\frac{132(18)}{10.38}(3.49)$

⇒ $\ 806.6$

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