Question 632404
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Let *[tex \LARGE x] represent the measure of one side of the base.  The surface area is comprised of 2 bases, each of which has an area of *[tex \LARGE x^2] and 4 sides, each of which has an area of *[tex \LARGE 5x], so the total surface area, which we know to be 48 *[tex \LARGE m^2], is described by the following equation:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 2x^2\ +\ 20x\ =\ 48]


A little algebra music, Sammy:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ x^2\ +\ 10x\ -\ 24\ =\ 0]


Solve the quadratic for the positive root.  Use this to calculate the area of the base of your prism.  Multiply the area of the base times the given height to find the volume.


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it
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