Finding surface area element of a right oblique cone in polar coordinates using integration

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I have this right angled oblique cone whose vertex is right angled with the diameter $2R$ and has a height $h$. I need to find the surface area element $dS$ for this cone. I know about the surface area of circular cone but the oblique cones seem difficult for me to understand about how to advance. It also needs to be computed in polar coordinates. Can someone help me in finding the surface area element $dS$ in terms of polar coordinates ($d\theta$ or $dr$)?