can you help me please with math

Question

x2 + y2 ≤ 9 and y ≥ |x|. What is the area of this region?

Answer 1

x² + y² ≤ 9 and y ≥ |x|. 

To visualize the area, I suggest to draw x2 + y² = 9 and y = |x|.

 

This is basically the area of the sector bounded by y=-x and y=x (from bottom) and x2 + y2 = 9 (from top). 

 

Area of Sector = θ /2* r² (here θ =π/2. I think you guess why)

So the area is (9/4)π. This is actually 1/4 of area of the circle x²+y²=9.