The area in square units of the circle whose center is at point P b. 9π .
Therefore , b. 9π is correct .
Since the area of the rectangle is 18 square units, and the sides of a rectangle are perpendicular to each other.
we know that the length of one side of the rectangle is 6 units and the length of the other side is 3 units.
The diameter of the circle is equal to the length of the diagonal of the rectangle, which we can find using the Pythagorean Theorem:
diagonal^2 = 6^2 + 3^2 = 45
diagonal = sqrt(45) = 3sqrt(5)
The radius of the circle is half of the diameter, so the radius is equal to 1.5sqrt(5).
area of circle = πr^2 = π(1.5sqrt(5))^2 = 9π/4 .
Therefore, the area of the circle is 9π/4 square units.