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Answer
The graph of |x+y| = 6 is two parallel lines whose equations are x+y = 6 and x+y = -6
The region |x+y| <= 6 is the region between the two parallel lines.
$$x^2 + y^2$$ <= 36 is the area inside the circle with center (0,0) and radius = 6.
So, the required area is the area of the circle - the areas of the segments cut off by the two chords x+y = 6 and x+y = -6
This area = $$\pi * 6^2/2 + 1/2 * 6 * 6 * 2 = 18\pi + 36 = 18(\pi + 2)$$
