document.write( "Question 1165476: The volume of a truncated prism with an equilateral triangle as its horizontal base is equal to 3600 cm3. The vertical edges at
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Algebra.Com's Answer #852160 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "The volume of a truncated prism with an equilateral triangle as its horizontal base is equal to 3600 cm3.
\n" ); document.write( "The vertical edges at each corner are 4, 6, and 8 cm. respectively. Find one side of the base.
\n" ); document.write( "a. 22.37 b. 25.43 c. 37.22 d. 17.89
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document.write( "First, let's look at the position of the point at the sloped section, \r\n" );
document.write( "which is exactly over the center of the regular triangle at the base.\r\n" );
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document.write( "Vertical coordinate of this point is the arithmetic mean of the numbers 4, 6 and 8\r\n" );
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document.write( "    z =  = 6 cm  over the base plane.\r\n" );
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document.write( "Now, let's accept without a proof, that the volume of the truncated prism is the same \r\n" );
document.write( "as the volume of the regular prism with the same base and the height of 6 sm.\r\n" );
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document.write( "If the side of the base is 'a', then the area of the base is   cm^2,\r\n" );
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document.write( "and the volume of the regular prism is   cm^3 =  cm^3.\r\n" );
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document.write( "It gives us an equation for 'a'\r\n" );
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document.write( "     = 3600.\r\n" );
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document.write( "From this equation\r\n" );
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document.write( "     =  =  =  = ,\r\n" );
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document.write( "    a =  = 37.22 cm  (rounded).\r\n" );
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document.write( "ANSWER.  The size of the base is about 37.22 cm ,  which is option (c)  in the answer list.\r\n" );
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