Answer:
Ac = (24- (s / 4)) ^ 2 / (4 pi)
Step-by-step explanation:
Because the piece is rope is divided into two pieces we have to:
c + s = 24, where c is the circumference of circle and s is the perimeter of square. Therefore the circumference of circle would be equal to:
c = 24-s
Let As the area of the square be, we know that the perimeter is the sum of all sides and a square has four sides, therefore the value of each side would be the perimeter divided by four. And the area of the square is a side raised to the square, as follows:
As = (s / 4) ^ 2
Now knowing that the circumference of circle is equal to the radius, by the number pi, by two, we have to:
c = 2 * pi * r
rearranging we have:
r = c / (2 * pi)
Let Ac be the area of the circle we have the radius squared by the number pi, like this:
Ac = pi * r ^ 2
But we already know the equivalence of the radius, replacing:
Ac = pi * (c / (2 * pi)) ^ 2
Now replacing the circumference of circle with its equivalence with the perimeter of the square we have to:
Ac = pi * ((24-s) / (2 * pi)) ^ 2
Now knowing that the one side of the square is equal to a quarter of the perimeter of the square we have:
Ac = (24- (s / 4)) ^ 2 / (4 pi)
That would be the area of the circle as a function of one side of the square.