SOLUTION: Two prism are constructed, one with its base a regular hexagon 6 in. on a side and the other with its base a rhombus whose diagonals are 12 inches and 9 inches. If their altitudes

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Question 1048810: Two prism are constructed, one with its base a regular hexagon 6 in. on a side and the other with its base a rhombus whose diagonals are 12 inches and 9 inches. If their altitudes are equal, compare their volumes.
Answer by ikleyn(52858) About Me  (Show Source):
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Two prism are constructed, one with its base a regular hexagon 6 in. on a side and the other with its base a rhombus
whose diagonals are 12 inches and 9 inches. If their altitudes are equal, compare their volumes.
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It is the same as to compare the areas of their bases. 

In the first case you have 6 (six) regular triangles at the base with the side of 6 in each.

So, their total area is 6%2A%281%2F2%29%2A6%2A6%2A%28sqrt%283%29%2F2%29 = 54%2Asqrt%283%29 sq.in.


In the second case you have 4 (four) right-angled triangles with the legs 6 in and 4.5 in.

Their total area is 4%2A%281%2F2%29%2A6%2A4.5 = 54 sq.in.


Can you make a conclusion based on this data?