Algebra.Com's Answer #518240 by Edwin McCravy(20060)![\"\"](\"/images/stars/stars-13.gif\")  
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VWXYZ is a rectangle-based pyramid where
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document.write( "WX = 66cm and XY = 32 cm. The vertex V is
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document.write( "vertically above the centre of the base.
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document.write( "Given that the slant heights VA and VB are
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document.write( "56 cm and 63 cm respectively, draw the net
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document.write( "of the pyramid and find its total surface
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document.write( "area. Also find the height and volume of
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document.write( "the pyramid.
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document.write( "Triangles WVZ and XYV have base 32 and altitude 63,\r\n" );
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document.write( "Each has area =  (32)(63) = 1008 cm²\r\n" );
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document.write( "Both together have area 2004 cm²\r\n" );
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document.write( "Triangles YZV and XYV have base 66 and altitude 56,\r\n" );
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document.write( "Each has area = (66)(56) = 1848 cm²\r\n" );
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document.write( "Both together have area 3696 cm²\r\n" );
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document.write( "The rectangular base has area (66)(32) = 2112\r\n" );
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document.write( "So the entire surface area of the pyramid is\r\n" );
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document.write( "2004 cm² + 3696 cm² + 2112 cm² = 7812 cm²\r\n" );
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document.write( "When triangle WZV is folded upwards so that vertex V\r\n" );
document.write( "is directly above O, then the right triangle OBV will \r\n" );
document.write( "have base OB = 33, (half of 66) and hypotenuse BV = 63.\r\n" );
document.write( "Using the Pythagorean theorem, \r\n" );
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document.write( "BV² = OB² + OV²\r\n" );
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document.write( "63² = 33² + OV²\r\n" );
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document.write( "3969 = 1089 + OV²\r\n" );
document.write( "2880 = OV²\r\n" );
document.write( " = OV\r\n" );
document.write( " = OV\r\n" );
document.write( " = OV, which is the height of the pyramid.\r\n" );
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document.write( "Checking, when triangle YZV is folded upwards so that \r\n" );
document.write( "vertex V is directly above O, then the right triangle OAV will \r\n" );
document.write( "have base OA = 16, (half of 32) and hypotenuse AV = 56. \r\n" );
document.write( "Using the Pythagorean theorem, \r\n" );
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document.write( "AV² = OA² + OV² (That's OV when the sides are folded up)\r\n" );
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document.write( "56² = 16² + OV²\r\n" );
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document.write( "3136 = 256 + OV²\r\n" );
document.write( "2880 = OV²\r\n" );
document.write( " = OV\r\n" );
document.write( " = OV\r\n" );
document.write( " = OV, which gives the same height of the pyramid.\r\n" );
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document.write( "So that checks out.\r\n" );
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document.write( "Height of the pyramid = OV = cm²\r\n" );
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document.write( "The volume is calculated by the formula\r\n" );
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document.write( "V =  =  =  cm³.\r\n" );
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document.write( "Edwin \n" );
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