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 # 2 #. If the angle between sides A and C is #(3 pi)/4 #, what is the area of the parallelogram?

1 Answer
Jun 7, 2016

area of given parallelogram is #1.4142#

Explanation:

Area of a parallelogram with sides #a# and #b# and included angle #theta# is given by #axxbxxsintheta#.

Note that in a parallelogram. while one angle is #theta#, other angle is #(180^o-theta)# and as #sin(180^o-theta)=sintheta#, which ever angle we may choose, area is not affected.

As two sides are #1# and #2# and included angle is #(3pi)/4# and

area of given parallelogram is

#1xx2xxsin((3pi)/4)=2xx1/sqrt2=sqrt2=1.4142#