Answer:
A = πr² ← r is the radius and r = \frac{1}{2} d ← d is the diameter
Hence
π (\frac{1}{2} d)² = A, that is
\frac{d^2\pi }{4} = A ( multiply both sides by 4 )
d²π = 4A ( divide both sides by π )
d² = \frac{4A}{\pi } ( take the square root of both sides )
d = \sqrt{\frac{4A}{\pi } }
