The area of a rectangle whose sides are 176 cm and 56 cm is equal to the area…

Concept: The area of a rectangle is length × breadth. For a circle of radius r, area = πr2 and circumference = 2πr. When two figures are stated to have equal areas, equating the two area expressions gives one equation in the unknown radius; once r is fixed, the circumference follows directly from 2πr. So an "equal-area" link is always solved in two moves: area → radius, then radius → the quantity asked for.

Application

1. Area of the rectangle = 176 × 56 = 9856 cm2.

2. The circle has the same area, so πr2 = 9856.

3. Substitute π = 22/7: (22/7) × r2 = 9856, hence r2 = (9856 × 7) ÷ 22 = 68992 ÷ 22 = 3136.

4. Take the positive square root: r = √3136 = 56 cm.

5. Circumference = 2πr = 2 × (22/7) × 56 = 2 × 22 × 8 = 352 cm.

Cross-check: put r = 56 back into the area formula — (22/7) × 3136 = 22 × 448 = 9856 cm2, exactly the rectangle’s area, so the radius is right. A second, independent route confirms the circumference without using π again: dividing circumference = 2πr by area = πr2 gives circumference = 2 × area ÷ r = 2 × 9856 ÷ 56 = 352 cm.

Result: the circumference of the circle is 352 cm.