Question

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?

Answer 1

`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`.