SOLUTION: the base of prism is an equilateral triangle of side 12cm. if the volume of the prism is 1080cc then the total surface area of prism

Question 802957: the base of prism is an equilateral triangle of side 12cm. if the volume of the prism is 1080cc then the total surface area of prism
Answer by thejackal(72) (Show Source): You can put this solution on YOUR website!
first you should break down your problem
Surface Area of the prism = 2 * Area of Triangle + 3 * Area of rectangle
Lets start by getting the area of the equilateral triangle which can be expressed as
(s^2 . root(3))/4 this is faster than 1/2bh since we don't know h and would otherwise have to calculate it.
so area of the triangle is (12^2*root(3))/4 = 62.354 cm2
thus the surface area of the sides of the prism is 62.354*2 = 124.708cm2
Now lets find the area of the rectangle:
we are given the volume which can be expressed as the base area * height
the height is the length of the rectangle so
1080 = 62.354 * h therefore h = 1080/62.354 = 17.32cm
so the surface area of the rectangle is 17.32*12; since there are 3 such rectangles the surface area of all is 17.32*12*3 = 623.54cm2
go back to our 1st equation to finally get the total surface area as 124.708 + 623.54 = 748.2 cm2

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