document.write( "Question 1083749: The base of a right pyramid is a regular hexagon with sides of length 10 m. The altitude is 5 m. Find the total surface area of the pyramid.
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Algebra.Com's Answer #697979 by ikleyn(52813) $\"\"$ $\"About$

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\n" ); document.write( "The base of a right pyramid is a regular hexagon with sides of length 10 m. The altitude is 5 m. Find the total surface area of the pyramid.
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document.write( "0.  Make a sketch to follow my arguments.\r\n" );
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document.write( "    Draw the pyramid, its base and its altitude.\r\n" );
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document.write( "1.  The total surface area is the sum of the base area and the lateral area.\r\n" );
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document.write( "    The base area is the area of the regular hexagon with the side length of 10 m.\r\n" );
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document.write( "    This hexagon is the union of 6 regular triangles with the side length of 10 m.\r\n" );
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document.write( "    Hence, the base area is  =  .\r\n" );
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document.write( "2.  The lateral area is 6 times the area of one lateral face. \r\n" );
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document.write( "    Each lateral face is a triangle with the base of 10 m long.\r\n" );
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document.write( "    Consider the slant height of the pyramid, which is the height of the triangular lateral face.\r\n" );
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document.write( "    This slant height is the hypotenuse of the right-angled triangle with the legs of 5 m (the altitude of the pyramid) and \r\n" );
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document.write( "     =  (the apothem of the regular hexagon at the base).\r\n" );
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document.write( "    Hence, the slant height length is  = 10 m.\r\n" );
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document.write( "    Then the area of each triangular lateral face is  = 50 m^2 and the area of 6 such lateral faces is 6*50 = 300 m^2.\r\n" );
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document.write( "4.  Thus the total surface area of the pyramid is   .\r\n" );
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