a 12x12-inch square is divided into n^2 congruent squares by equally spaced lines parallel to its sides. circles are inscribed in each of the squares. find the sum of the areas of the circles... please answer and explain how you got this answer!!!

Answer 1

if there are n squares per side, each square is 12/n inches square.

For a square of side s, the inscribed circle has radius s/2.

So, the circles add up to

n^2 (pi (12/2n)^2) = pi n^2 36/n^2 = 36pi

Note that it is the same area as for a single inscribed 6-inch circle!