Suppose I have parallelograms of same sides say 5 and 10 units with different left-bottom angle as $\frac{\pi}{6}$, $\frac{\pi}{4}$, $\frac{\pi}{3}$, $\frac{\pi}{2}$. What is the comparison between the areas? I have the intuition that the area is increasing in this order. If this is correct, where does the area go if angle is decreased from $\frac{\pi}{2}$.
What about the same if they are considered on the inner side and outer side of a hollow sphere ball?
HINT:
The area of a parallelogram with adjacent sides $a,b$ and the angle between them being $C$
will be $ab\sin C$