document.write( "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 \n" ); document.write( "

Algebra.Com's Answer #484076 by thejackal(72) $\"\"$ $\"About$

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first you should break down your problem\r
\n" ); document.write( "\n" ); document.write( "Surface Area of the prism = 2 * Area of Triangle + 3 * Area of rectangle\r
\n" ); document.write( "\n" ); document.write( "Lets start by getting the area of the equilateral triangle which can be expressed as\r
\n" ); document.write( "\n" ); document.write( "(s^2 . root(3))/4 this is faster than 1/2bh since we don't know h and would otherwise have to calculate it. \r
\n" ); document.write( "\n" ); document.write( "so area of the triangle is (12^2*root(3))/4 = 62.354 cm2
\n" ); document.write( "thus the surface area of the sides of the prism is 62.354*2 = 124.708cm2\r
\n" ); document.write( "\n" ); document.write( "Now lets find the area of the rectangle:\r
\n" ); document.write( "\n" ); document.write( "we are given the volume which can be expressed as the base area * height\r
\n" ); document.write( "\n" ); document.write( "the height is the length of the rectangle so \r
\n" ); document.write( "\n" ); document.write( "1080 = 62.354 * h therefore h = 1080/62.354 = 17.32cm\r
\n" ); document.write( "\n" ); document.write( "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\r
\n" ); document.write( "\n" ); document.write( "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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