document.write( "Question 399602: One angle of a parallelogram is 120 degrees,and two consecutive sides have lengths of 8 inches and 15 inches. What is the area of the parallelogram? \n" ); document.write( "
Algebra.Com's Answer #282981 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
One angle of a parallelogram is 120 degrees,and two consecutive sides have lengths of 8 inches and 15 inches. What is the area of the parallelogram?
\n" ); document.write( "
\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Since two adjacent angles of a parallelogram are supplementary, we find\r\n" );
document.write( "that the lower left angle is 180°-120° = 60°:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Area = base × height\r\n" );
document.write( "\r\n" );
document.write( "We have the base, which is 15 inches, but we need the height, the\r\n" );
document.write( "ACTUAL height, not the length of the slanted sides.  So we draw a \r\n" );
document.write( "perpendicular from a vertex to the opposite side.  I'll draw it\r\n" );
document.write( "in green and label it h:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The right triangle on the left has a 60° angle, therefore it is a\r\n" );
document.write( "30°60°90° right triangle, and therefore its shorter side (the bottom\r\n" );
document.write( "side) is \"1%2F2\" the length of the hypotenuse, and \"1%2F2\" of 8 is\r\n" );
document.write( "4. so the bottom side of the quadrilateral has been split into\r\n" );
document.write( "two parts, 4 inches and 11 inches:\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "We now use the Pythagorean theorem to calculate the length of the\r\n" );
document.write( "green altitude:\r\n" );
document.write( "\r\n" );
document.write( "\"a%5E2%2Bb%5E2=c%5E2\"\r\n" );
document.write( "\"4%5E2%2Bh%5E2=8%5E2\"\r\n" );
document.write( "\"16%2Bh%5E2=64\"\r\n" );
document.write( "\"h%5E2=48\"\r\n" );
document.write( "\"h=sqrt%2848%29\"\r\n" );
document.write( "\"h=sqrt%2816%2A3%29\"\r\n" );
document.write( "\"h=sqrt%2816%29%2Asqrt%283%29\"\r\n" );
document.write( "\"h=4sqrt%283%29\"\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "                                              __\r\n" );
document.write( "Now we have the height of the parallelogram 4√3, and we know the base of\r\n" );
document.write( "the parallelogram is 15.\r\n" );
document.write( "\r\n" );
document.write( "Since \r\n" );
document.write( "\r\n" );
document.write( "Area = base × height,\r\n" );
document.write( "               __\r\n" );
document.write( "Area = 15 × 4√3\r\n" );
document.write( "          __\r\n" );
document.write( "Area = 60√3 square inches\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );