a simple but interesting problem of prism...

Geometry Level 1

A prism has volume 100 cm³ and length 8 cm . If the cross section is an equilateral triangle, find the length of a side of the triangle. Please share if you have a easier or better solution.


The answer is 5.37.

Abhijit Das by Abhijit Das , 25, Bangladesh

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2 solutions

Volume of a prism is V=Bh where B denotes the area of the base and h is the height. Area of an isosceles triangle is A=1/2 a^2 sin60 where a is the side. Therefore 100=(1/2 a^2 sin60)*8; solving for a will give you 5.37.

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Ori Ashual
Sep 16, 2014

the formula for the volume of a prism is V = A h where A is the base triangle area and h is the height (or length) of the prism. 100 = 8 A that means A = 12.5 the triangle is equilateral so it's area formula is : a^2 * sqrt(3) / 4 where a is the side so we have: a^2 * sqrt(3) / 4 = 12.5 a^2 * sqrt(3) = 50 a^2 = 50/sqrt(3) = 28.86 a = 5.37

its my first time posting a solution so sorry for the messy description

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