Question 1048810
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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.


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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*(1/2)*6*6*(sqrt(3)/2)}}} = {{{54*sqrt(3)}}} 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*(1/2)*6*4.5}}} = 54 sq.in.


Can you make a conclusion based on this data?
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