SOLUTION: A chocolate company has a new candy bar in the shape of a prism whose base is a 1 inch equilateral triangle whose sides are rectangles that measure 1 inch by 2 inches. These prisms

Question 1163368: A chocolate company has a new candy bar in the shape of a prism whose base is a 1 inch equilateral triangle whose sides are rectangles that measure 1 inch by 2 inches. These prisms will be packed in a box that has a rectangular hexagonal base with 2 inch edges, and rectangular sides that are 6 inches tall. How many candy bars will fit in such a box?
Answer by ikleyn(52795) (Show Source): You can put this solution on YOUR website!
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Mark the center O of the regular hexagon at the base and connect the center with two consecutive vertices A and B of the hexagon.


You will get an equilateral triangle AOB with the side length of 2 inches.


You can place 4 equilateral triangles with the side length of 1 unit inside the triangle AOC.


Next, take into account that the hexagonal base comprise of 6 such triangles congruent to triangle AOB.


It means that you can place 6*4 = 24 small triangles inside the hexagon base.


You then multiply this number, 24, by 2 to account for the height of the package and the height of the candy bar.


So your answer is 24*2 = 48 candy bars in one package.

Solved.

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