A parallelogram has sides A, B, C, and D. Sides A and B have a length of 8 and sides C and D have a length of 9 . If the angle between sides A and C is pi/4 , what is the area of the parallelogram?

1 Answer
Jan 30, 2016

36 sqrt2 " units"^2

Explanation:

Area of a parallelogram is the product of the base and the height. We know that the length of the base is 9. The height may be calculated by the sine of the angle between the sides. Thus,

h / ("side" A) = sin( pi/4 ) = 1 / sqrt2
=> h = ( 8 " units" ) / sqrt(2) = 4 sqrt2 " units"

Thus, the required area is A = 9 " units" * 4 sqrt2 " units" = 36 sqrt2 " units"^2 .