Question

Find the area of the figure above

Answer 1

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.


`\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`