Question

A parallelogram has sides A, B, C, and D. Sides A and B have a length of `2` and sides C and D have a length of `7`. If the angle between sides A and C is `pi/4`, what is the area of the parallelogram?

Answer 1

The area of the parallelogram is equal to the cross product of the vectors representing, `vec(A) and vec(C)`,
`A_diamond=vec(A)xxvec(C)= |A||C| sin(pi/4)`
`A_diamond= |A||C| sin45^o = 2*7*sqrt(2)/2=7sqrt(2)`

Explanation:

Given a parallelogram has side with `A=B=2` and C=D=7
Angle between `A and C, alpha=pi/4`
Required Area, `A_(diamond)` of parallelogram?
Definition and Principles:
`Area_diamond= |A||C| sin(pi/4) =|A||C| sin45^o = 2*7*sqrt(2)/2=7sqrt(2)`