document.write( "Question 253190: How do you find the area of a parallelogram with sides 8 and 14 and an included angle of 60 degrees? \n" ); document.write( "

Algebra.Com's Answer #185422 by richwmiller(17219) $\"\"$ $\"About$

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Draw your parallelogram with sides 8 and 14 with angle of 60 degrees with the 60 angle at the base on the left.
\n" ); document.write( "If one angle is 60 the opposite angle is also 60.
\n" ); document.write( "The remaining angles are 120 each.
\n" ); document.write( "Now draw the height (altitude) from the 120 angle to the base .
\n" ); document.write( "We now have a right triangle with angles 30 60 90. We know that the sides in a 30 60 90 triangle are proportioned 1:sqrt(3):2
\n" ); document.write( "Now since the hypotenuse is 8 the triangles proportions are multiplied by 4.
\n" ); document.write( "so the altitude is 4sqrt(3)
\n" ); document.write( "We are not told where the 60 degree angle is.
\n" ); document.write( "I choose to make the base 14 and the altitude is 4sqrt
\n" ); document.write( "So the area is base times height which is 14*4sqrt(3)=64sqrt(3)
\n" ); document.write( "If the base is 8 then the height is 7sqrt(3) and the area is 8*7sqrt(3) or 56sqrt(3) \n" ); document.write( "

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