Question

Find the area of the figure​

Answer 1

Check the picture below.

so the figure is really a 6x21 rectangle, a 2x2 square, and a couple of quarter of a circle whose radius is 2, now, if put two quarters together, we get half, so both of those quarter circles add up to just a semi-circle with a radius of 2.

$\stackrel{\textit{\huge Areas}}{\stackrel{rectangle}{(6)(21)}~~ + ~~\stackrel{square}{(2)(2)}~~ + ~~\stackrel{two~\frac{1}{4}~circle}{\cfrac{1}{2}\pi (2)^2}}\implies 126+4+2\pi \implies 130+2\pi$