The beautiful hand drawn picture below shows the dreadful situation.

The intersections points are,

thus, .

Now we find the perimeter below and perimeter above.

1)Perimeter above is easy, simply .

2)The Perimeter below is,

Thus,

Let,

then subsitution rule yields,

Ignoring the limits of integration let us find the anti-derivative of,

Express as,

Let,

then,

Also,

then,

Thus,

Can you take it from here?

Integrate that then substitute once you finish.