The area of a square is the square of the length of its side. Here, we're told that the side of each square is equal to the radius (r) of the circle. Then the area of each square is .. Asquare = r^2 There are 3 of them, so their total area is .. Aall_squares = 3*r^2
The area of a circle is given by the formula .. Acircle = π*r^2 . . . . . where r represents the radius of the circle
Fernie wants to compare the area of the 3 squares to that of the circle. We know that the value of π is about 3.1416, a little more than 3, so we have .. Aall_squares = 3*r^2 .. Acircle ≈ 3.1416*r^2
We notice that 3.1416 is more than 3, so the area of the circle is greater than the area of Fernie's 3 squares.
___ It is not clear to me that Fernie's drawing will explain the formula A = π*r^2, unless it can somehow be used to show that the parts of each square that are outside the circle add up to an amount that is slightly less than the uncovered part of the circle.
