Let the side of square be of length '2a'
For the largest circle carved out of the square sheet, radius will be 'a' and hence the required area of circle = PI(a2)
For a given perimeter, the circle has the largest area possible.
A circle with a diameter of 2 is the guiding cynosure when Pi is the square of all possible circles: If the square root of Pi defines the side of a square and that square can be inscribed within a circle or enclose a circle, then the diameters of all possible circles between the largest and smallest include the circle of which Pi is its perfect square (a diameter of 2).
The largest diameter you can inscribe in a circle is a square. The square's diagonal is equal to the diameter of the circle; the length of the side of the square is therefore equal to the circle's diameter, divided by the square root of 2.
You mean the largest possible area with a perimeter of 18, right? Well, the largest area is with a circle, which has area 81/pi which is approximately 25.7831 If you need a rectangular area, the largest is a square of width=length (definition of square) = 4.5 This has area 4.52 which is 20.25, substantially less than the circles area...
Half the length of a side of the square.
Of course, it is not possible !
The radius of the largest circle that fits in a 176-yd square is 88 yds.
The largest square that could fit in a circle of diameter 10 inches has dimensions 5sqrt(2) inches by 5sqrt(2) inches.
The circle. Next comes the square.
Largest area = pi*182 = 1017.876 square cm to 3 dp
The largest rectangle would be a square. If the circle has radius a, the diameter is 2a. This diameter would also be the diameter of a square of side length b. Using the Pythagorean theorem, b2 + b2 = (2a)2. 2b2 = 4a2 b2 = 2a2 b = √(2a2) or a√2 = the length of the sides of the square The area of a square of side length b is therefore (√(2a2))2 = 2a2 which is the largest area for a rectangle inscribed in a circle of radius a.
The is not stated that the circle inside the square was the greatest possible circle, so all one can say is 8pi at most.