The area of a square is 𝑑. What is the area of the circle which has the…

Solution: Derive the circle area from the square's area step by step.

• Let the side length of the square be s. Since the square's area is d, we have s = √d.

• The diagonal of the square is s·√2 = √d · √2 = √(2d). This diagonal is the circle's diameter.

• Radius of the circle r = (diameter)/2 = √(2d)/2.

• Area of the circle = π·r² = π·(√(2d)/2)² = π·(2d)/4 = (1/2)·π·d.

Therefore the area of the circle is (1/2)·π·d.