Calculate the area of this object problem

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Stuck on the last questions of my homework that's due in tomorrow. Somebody help. I think it's to do with integration but i can't do it. Can anyone give me a hint?Problem

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Hint: Join the centre to the $4$ corners of the orange (?) figure. That divides the figure into $4$ equal parts. Let's find the area of one of the parts, say the "top" one.

Draw horizontal and vertical axes through the centre. The top line of the square is $y=1$.

For reasonable $x$ and $y$, the point $(x,y)$ is on the top curvy part of the boundary if $1-y=\sqrt{x^2+y^2}$. This is the parabola $2y=1-x^2$.

The rest is calculation of a kind you are expected to be able to do,