To solve the problem shown in the figure attached, you must apply the proccedure shown below:
1. You have that the equation for calculate the area of a circle is:
A=πr²
2. You have that the formula for calculate the diameter of a circle is:
d=2r
Therefore, the radius is r=d/2
where r is the radius of the circle
3. Keeping the information above on mind, you have the correct sequence of the equations by clearing the diameter d, is shown below:
A=π(d/2)²
A=πd²/4
4A=πd²
d²=4A/π
d√(4A/π)
Therefore, as you can see, the answer is:
A=π(d/2)²
A=πd²/4
4A=πd²
d²=4A/π
d√(4A/π)