Area of lit part of a truncated paraboloid

A truncated paraboloid is given by

$z = x^2 + y^2 \text{, where } 0 \le z \le 4$

Its surface is made of an opaque material. It is lit by a single point omni-directional light source (omni-directional means radiating light in all directions).

What is the area of the paraboloid lit by the point light source that is positioned at $(3, 4, 5)$ ?

Note: Most of the lit surface is lit externally, but there is another part of the paraboloid that is lit on the inside surface through the circular hole that is at the top. Report the sum of both areas.

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