A wire is bent to form a circle of radius 56 cm. If the same wire is then bent to form a square, what will be the area of that square in square centimetres (sq cm)?

Introduction:
This problem tests perimeter conservation: when a wire is reshaped, its length remains the same. The wire first forms a circle of radius 56 cm, so its length equals the circumference of that circle. When reshaped into a square, the same wire length becomes the perimeter of the square. From the perimeter, we find the side length and then compute the square’s area. Because pi is involved, we commonly use pi = 22/7 to get an exact integer result when the numbers are chosen nicely, as they are here.

Given Data / Assumptions:

• Circle radius r = 56 cm• Wire length is constant• Use pi = 22/7 for exact computation

Concept / Approach:
Wire length = circumference of circle = 2*pi*r. This becomes perimeter of square = 4s. Set 4s = 2*pi*r, solve for s, then area = s^2.

Step-by-Step Solution:
Step 1: Compute circumference of the circle.Circumference = 2*pi*r = 2*pi*56 = 112*piStep 2: This is equal to perimeter of the square.4s = 112*piStep 3: Solve for side s.s = (112*pi)/4 = 28*piStep 4: Substitute pi = 22/7.s = 28*(22/7) = 4*22 = 88 cmStep 5: Compute area of the square.Area = s^2 = 88^2 = 7744 sq cm

Verification / Alternative check:
Perimeter of the square would be 4*88 = 352 cm. Circumference of the circle using pi=22/7 is 2*(22/7)*56 = (44/7)*56 = 44*8 = 352 cm. They match exactly, confirming that the same wire length is used, so the area 7744 sq cm is consistent.

Why Other Options Are Wrong:
8844 and 7056 would correspond to different side lengths, which would break the fixed-perimeter condition.5544 and 4444 are far too small and imply a shorter wire than the circle provides.Only 7744 matches side 88 derived from the correct circumference-to-perimeter conversion.

Common Pitfalls:
• Using area formula of circle instead of circumference for wire length.• Forgetting that square perimeter is 4s.• Using pi incorrectly or not simplifying 28*(22/7) properly.

Final Answer:
The area of the square is 7744 sq cm.