Answer:
[tex]First~part:\\Radius~of~big~circle(R) = 6\\Radius~of~small~circle(r)=x\\Now,\\Area ~of~ border ~= Area ~of~ big~ circle - area~ of~ small~ circle\\~~~~~~~~~~~~~~~~~~~~~~~=\pi R^{2} - \pi r^2 = \pi (6)^2-\pi r^2\\~~~~~~~~~~~~~~~~~~~~~~~= \pi (6^2-r^2)\\~~~~~~~~~~~~~~~~~~~~~~~=\pi (36+r)(36-r)[/tex][tex]Second part:\\Length~of~big~square~carpet (L) =x\\Length~of~small~square~carpet (l) = 2y\\Now,\\Area~of~the~carpeted~floor = Area~ of~ big ~square~ carpet - area ~of ~small~ square~ carpet\\~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~=L^2-l^2 = x^2-4y^2 =(x+2y)(x-2y)[/tex]
