The figure shows a region consisting of all points inside a

The figure shows a region consisting of all points inside a square that are closer to the center than to the sides of the square. Find the area of the region

Solution

given the figure has its perimeter as all those points which are closer to the centre than to the sides of the square let centre be (0,0) and eqns if sides be |x|=1 and |y| =1 i.e. x= 1, x=-1, y=1 and y = -1 and let the point be (p,q) p^2 +q^2 < (p-1)^2 /1^2 =( q^2 +2p -1<0) p^2 +q^2 < (p +1)^2 /1^2=( q^2 -2p -1<0) and p^2 +q^2 < (q-1)^2/1^2 =( p^2 +2q -1<0) p^2 +q^2 < (q+1)^2/1^2=( p^2 -2q -1<0)