Area of the intersection of two regions in the plane

[Mr Davis 97]

I have two regions, given by $y>\sqrt{2}x - \frac{1}{4x}$ and $y< \sqrt{2}x + \frac{1}{4x}$. How can I find the area of their intersection? If their is no easy analytical way, could someone perhaps use a computer? I am not sure how.

 

[BvU]

area of their intersection

What do you mean with that ? There is no intersection.
You mean the area between the two curves ?
If this is homework, the PF guidelines require an attempt at solution fom your part