document.write( "Question 1018062: The base of a prism is a quadrilateral whose sides are 3.5 cm, 4 cm, 5 cm , and 6 cm. Its shorter diagonal is 6 cm.long. If the altitude is 20 cm., find its volume. \n" ); document.write( "

Algebra.Com's Answer #634451 by Edwin McCravy(20065) $\"\"$ $\"About$

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document.write( "Below is the quadrilateral ABCD which is the base of the prism.\r\n" );
document.write( "The green line is the shorter diagonal.\r\n" );
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document.write( "The volume of a prism is the area of the base multiplied\r\n" );
document.write( "by the height, or altitude.\r\n" );
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document.write( "We know the altitude is 20 cm.  We need the area of the\r\n" );
document.write( "quadrilateral ABCD base.  This quadrilateral's area is the \r\n" );
document.write( "sum of the areas of triangles ABC and ACD.\r\n" );
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document.write( "We will use Heron's formula for the area of a triangle:\r\n" );
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document.write( ", where\r\n" );
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document.write( "For triangle ABC,  \r\n" );
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document.write( "For triangle ACD,  \r\n" );
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document.write( "Add the two triangles' areas:\r\n" );
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document.write( "6.726521668 + 13.63589014 = 20.36241182 cm²\r\n" );
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document.write( "Multiply by the given altitude = 20 cm to get the desired volume:\r\n" );
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document.write( "(20.36241182 cm²)(20 cm) = 407.2482362 cm³\r\n" );
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document.write( "Edwin

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