document.write( "Question 924792: Consider a right pyramid that has 12 edges. The base of this pyramid is a regular polygon. the length of the sides in the base are 6cm. The slant height is 8cm. Draw a net of this pyramid, find the surface area and the volume of the figure. \n" ); document.write( "
Algebra.Com's Answer #561259 by Edwin McCravy(20059)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "To find the area we need the height and the area of the base.\r\n" );
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document.write( "The triangle with two blue sides in equilateral, so\r\n" );
document.write( "the blue lines are 6cm each.\r\n" );
document.write( "we can use the Pythagorean theorem to calculate the\r\n" );
document.write( "length of the red line\r\n" );
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document.write( "\"red%28red%29%5E2%2B3%5E2=blue%28blue%29%5E2\"\r\n" );
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document.write( "\"red%28red%29%5E2%2B9=6%5E2\"\r\n" );
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document.write( "{{red(red)^2+9=36}}}\r\n" );
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document.write( "{{red(red)^2=36-9}}}\r\n" );
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document.write( "{{red(red)^2=27}}}\r\n" );
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document.write( "\"red%28red%29=sqrt%2827%29\"\r\n" );
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document.write( "\"red%28red%29=3sqrt%283%29\"\r\n" );
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document.write( "So the area of the equilateral triangle is\r\n" );
document.write( "\"expr%281%2F2%296%2A3sqrt%283%29=9sqrt%283%29\"\r\n" );
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document.write( "The base is 6 or those equilateral triangles, which you\r\n" );
document.write( "can see from this:\r\n" );
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document.write( "So the area of the base of the pyramid is 6 times\r\n" );
document.write( "the area of one equilateral triangle:\r\n" );
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document.write( "Area of base = \"6%2A9sqrt%283%29=54sqrt%283%29\"\r\n" );
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document.write( "Now we need the height of the pyramid: \r\n" );
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document.write( "Now when the top triangle is folded up so that the\r\n" );
document.write( "green line hovers directly over the red line, the\r\n" );
document.write( "green line will become a hypotenuse, the red line\r\n" );
document.write( "will become a leg, and the height of the pyramid\r\n" );
document.write( "will be the other leg.  So we find the height of\r\n" );
document.write( "the pyramid by\r\n" );
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document.write( "\"green%28green%29%5E2=red%28red%29%5E2%2Bheight%5E2\"\r\n" );
document.write( "\"8%5E2=27%2Bheight%5E2\"\r\n" );
document.write( "\"64=27%2Bheight%5E2\"\r\n" );
document.write( "\"37=height%5E2\"\r\n" );
document.write( "\"sqrt%2837%29=height\"\r\n" );
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document.write( "volume of the pyramid is\r\n" );
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document.write( "cm3\r\n" );
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document.write( "Area of each triangle in the face is \r\n" );
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document.write( "\"expr%281%2F3%29%2A6%2A8=16\"\r\n" );
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document.write( "So since there are 6 faces, the surface area is \"6%2A16=96\" cm2\r\n" );
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document.write( "Edwin
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