![\"\"](\"/images/stars/stars-10.gif\")
You can put this solution on YOUR website!
\n" ); document.write( "
\r\n" ); document.write( " F ____E\r\n" ); document.write( " /\ /\\r\n" ); document.write( " A/__\/__\D\r\n" ); document.write( " \ /\ /\r\n" ); document.write( " \/__\/\r\n" ); document.write( " B C\r\n" ); document.write( "
\n" ); document.write( "Length AD=36 inches
\n" ); document.write( "Let the point of intersection of all the lines in the centre be O
\n" ); document.write( "
\n" ); document.write( "
\n" );
document.write( "Now,AO=OD=1/2 of AD
\n" );
document.write( "Then AO=(1/2)36=18 inches
\n" );
document.write( "Similarly,AO=BO=CO=DO=EO=FO
\n" );
document.write( "
\n" );
document.write( "For a polygon with 'n' sides,the exterior angle is given by the formula:
\n" );
document.write( "
\n" );
document.write( "For a hexagon,exterior angle=360/6=60 degrees
\n" );
document.write( "Therefore the interior angle is given by:
\n" );
document.write( "
\n" );
document.write( "Hence for a hexagon,interior angle is 180-60=120 degrees.
\n" );
document.write( "
\n" );
document.write( "Therefore the angles for the hexagon is 120 degrees
\n" );
document.write( "
\n" );
document.write( "Hence angle ABC=BCD=CDE and so on for all the angles for the hexagon.
\n" );
document.write( "Then angle ABO=angle OBC=half of angle ABC
\n" );
document.write( "So angle ABO=(1/2)120=60 degrees
\n" );
document.write( "
\n" );
document.write( "Now look at triangle AOB
\n" );
document.write( "
\r\n" ); document.write( " O\r\n" ); document.write( " /\\r\n" ); document.write( " / \\r\n" ); document.write( " A----B\r\n" ); document.write( "
\n" ); document.write( "Here,AO is equal to BO (proved earlier)
\n" ); document.write( "and angle ABO is 60 degrees.
\n" ); document.write( "Angle OAB is also 60 degrees (proved above)
\n" ); document.write( "
\n" );
document.write( "Now the angle at the center O is 360 degrees,divided into 6 parts.
\n" );
document.write( "Hence each part is 60 degrees.
\n" );
document.write( "This means angle AOB=60 degrees
\n" );
document.write( "
\n" );
document.write( "Then in triangle AOB,all three angles are 60 degrees.
\n" );
document.write( "It is an equilateral triangle with all equal angles,hence all its sides are also equal.
\n" );
document.write( "We know sides OA=OB.
\n" );
document.write( "Then side AB will also be equal to AO and OB
\n" );
document.write( "Therefore AB=18 inches.
\n" );
document.write( "This is the length of the side of the hexagon=18 inches
\n" );
document.write( "
\n" );
document.write( "Angle=120 degrees,Side=18 inches
\n" );
document.write( "
\n" );
document.write( "Hope this helps,
\n" );
document.write( "Prabhat