Homework Problem:
What is the largest possible area for a parallelogram that has pairs of sides with lengths 5 and 11?
R(subscript)max=?
Thanks
The area of the parallelogram is
$\displaystyle \displaystyle \begin{align*} A &= a\,b\sin{\theta} \\ &= 5 \cdot 11 \cdot \sin{\theta} \\ &= 55\sin{\theta} \end{align*}$
Since this is a sine function that has not been translated vertically, its maximum value is equal to its amplitude.