Thanks Chris 
Zetico have you done calculus yet - were you expected to do it a differerent way?
I decided to do it independently of Chris.
I tried a variety of ordinary geometry methods but eventually I also resorted to calculus.
Our answers are the same but maybe our methods are a little different. 
Let the bottom corner is the point (0,0)
Each of these curves is a quadrant. I am only interested in the quadrant centred at (0,0)
The equation is
$$\\x^2+y^2=1\\
y^2=1-x^2\\
y=\sqrt{1-x^2}\\\\
When \;\;x=0.5\;\;y=\sqrt{1-0.25}=\sqrt{0.75}\\\\
$The top intersection point is $(0.5,\sqrt{0.75})\\\\
$The right most intersection point is (\sqrt{0.75},0.5)\\\\
0.25* Area=\int_{0.5}^{\sqrt{0.75}}\;(\sqrt{1-x^2}-0.5 )\;\;dx\\\\
Area=4*\int_{0.5}^{\sqrt{0.75}}\;(\sqrt{1-x^2}-0.5 )\;\;dx\\\\
Area\approx 0.315147\;units^2$$
I also used wolfram alpha to do the calculation but maybe i could do it without wolfram|alpha if I had to :/
+118735 