Baby rudin example 10.32

Question

This is the definition which we need for this example : .

There is the example:

I don't understand why is $\partial\Sigma$ equal to $\Sigma(\partial D)$ and then why is $\Sigma$($\partial D$) equal of $\gamma_1 + \gamma_2 + \gamma_3 + \gamma_4$.

Any help would be appreciated.