check the picture below.
notice, all we really have is a semi-circle with a radius of 6, a 40x12 rectangle and a triangle whose base is 12 and height is 5.
we can simply get the area of each and sum them up, and that's the area of the composite.
[tex]\bf \stackrel{semi-circle}{\cfrac{\pi r^2}{2}}~~+~~\stackrel{rectangle}{length\cdot width}~~+~~\stackrel{triangle}{\cfrac{1}{2}bh}
\\\\\\
\stackrel{semi-circle}{\cfrac{\pi 6^2}{2}}~~+~~\stackrel{rectangle}{12\cdot 40}~~+~~\stackrel{triangle}{\cfrac{1}{2}(12)(5)}
\\\\\\
18\pi +480+30\implies 18\pi +510\quad \approx\quad 566.52[/tex]
