Find the surface area
1 answer:
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.
You might be interested in