document.write( "Question 1191007: Could you help me with this problem, please? I greatly appreciate your time and effort.\r
\n" ); document.write( "\n" ); document.write( "The cube shown has a side length of 6. Find the volume of the pyramid that has triangle BDE as its base and A as its vertex.\r
\n" ); document.write( "\n" ); document.write( "\"IMG-8701\" \n" ); document.write( "
Algebra.Com's Answer #822754 by ikleyn(52810)\"\" \"About 
You can put this solution on YOUR website!
.
\n" ); document.write( "Could you help me with this problem, please? I greatly appreciate your time and effort.
\n" ); document.write( "The cube shown has a side length of 6. Find the volume of the pyramid that has triangle BDE as its base and A as its vertex.
\n" ); document.write( "~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "
\r\n" );
document.write( "Let the length of an edge of the cube be  \"a\".\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "To calculate the volume, consider triangle ABE as a base of a pyramid BDEA \r\n" );
document.write( "\r\n" );
document.write( "and edge AD as the height of the pyramid (same as its altitude).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Use the formula for the volume of a pyramide\r\n" );
document.write( "\r\n" );
document.write( "    volume = 1/3 of the base area times the height = \"%281%2F3%29%2A%281%2F2%29%2Aa%2Aa%2Aa\" = \"%281%2F6%29%2Aa%5E3\" = \"%281%2F6%29%2A6%2A6%2A6\" = 36 cubic units.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Thus the volume of the pyramid BDEA is 1/6 of the volume of the cube  \"a%5E3\" = \"6%5E3\" = 216 cubic units.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "ANSWER.  The volume of the pyramid BDEA is  36  cubic units, which is  1/6  of the volume of the cube.\r\n" );
document.write( "
\r
\n" ); document.write( "\n" ); document.write( "Solved.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "------------------\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Comment from student :   Hello,  I was going through your solution again and realized you are asking
\n" ); document.write( "to consider the triangle  ABE  as a base of a pyramid but the question specifies that the base of pyramid is triangle  BDE.
\n" ); document.write( "Could you please help me taking into consideration that base is triangle  BDE  and not  ABE?\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "My response :   In this problem,  you can consider  (and can call)  ANY  FACE  with vertex  A  of the pyramid  BDEA  as a base of the pyramid.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Then the corresponding altitude will be the edge perpendicular to this base.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );