Find the area satisfying |x+y|<=6 and x^2+y^2<=36?(explain pls...)

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 = $$\pi * 6^2/2 + 1/2 * 6 * 6 * 2 = 18\pi + 36 = 18(\pi + 2)$$