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Answer:
6 tiles.
Step-by-step explanation:
We have been given that Roberto needs some roofing tiles to be cut from a large tile.
Let us find the number of tiles that can be cut from a larger piece of tile.
Let us convert our given mixed fractions in improper fractions.
Now let us substitute our given values in above formula.
Since we know that dividing a fraction by a fraction is same as multiplying the reciprocal of second fraction with the first fraction.
Upon cancelling out 8 from numerator and denominator we will get,
We can see that number of tiles turns out to be 6.98, although it is very close to 7, but we cannot round our answer because the 7th tile will still be shorter than the required measure. Therefore, we can only cut 6 tiles of the required size from the given large tile.
If you notice, the figure has two hexagonal faces and 6 rectangles.
now the rectangles are just 4x9 each, so their area is just 6(4*9) for all 6.
the hexagons has a distance from the center perpendicular to a side of 7.8, namely the apothem is 7.8, and since each side is 9 km long, the perimeter is 9+9+9+9+9+9.
since the area of a regular polygon is (1/2)(apothem)(perimeter), we can simply get the area of those two hexagons and the area of the rectangles, sum them up, and that's the surface area of the hexagonal prism.
![\bf \stackrel{\textit{6 rectangles}}{6(4\cdot 9)}~~~~+~~~~\stackrel{\textit{2 hexagons}}{2\left[ \cfrac{1}{2}(7.8)(54) \right]}](https://tex.z-dn.net/?f=%5Cbf%20%5Cstackrel%7B%5Ctextit%7B6%20rectangles%7D%7D%7B6%284%5Ccdot%209%29%7D~~~~%2B~~~~%5Cstackrel%7B%5Ctextit%7B2%20hexagons%7D%7D%7B2%5Cleft%5B%20%5Ccfrac%7B1%7D%7B2%7D%287.8%29%2854%29%20%5Cright%5D%7D)
now the rectangles are just 4x9 each, so their area is just 6(4*9) for all 6.
the hexagons has a distance from the center perpendicular to a side of 7.8, namely the apothem is 7.8, and since each side is 9 km long, the perimeter is 9+9+9+9+9+9.
since the area of a regular polygon is (1/2)(apothem)(perimeter), we can simply get the area of those two hexagons and the area of the rectangles, sum them up, and that's the surface area of the hexagonal prism.