A parallelogram has sides A, B, C, and D. Sides A and B have a length of #1 # and sides C and D have a length of # 5 #. If the angle between sides A and C is #(5 pi)/12 #, what is the area of the parallelogram?

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Answer 1 · 2016-08-20T18:54:30

#5/4#(#sqrt6# +#sqrt2#)

Draw a sketch of the parallelogram
Drop a perpendicular from the end of the top side .
Now you have a triangle .
The known angle is #5/12##pi#

The hypotenuse is 5 and the opposite side is the height h
So sin(#5/12##pi#) =#h/5#

Sin(#5/12##pi#) = #1/4#(#sqrt6#+#sqrt2#)

Drawn this way our base is length 1

So the height X base is as given above