An acre is 4,840 square yards. 9 acres is therefore 43,560 sq yds. 1 mile is 1,760 yards. A square mile is therefore 3,097,600 sq yds = 640 acres. 1/2 mile is 880 yards. Circumference normally applies to circles, being the perimeter of a circle. It can sometimes be used to mean the perimeter, or the distance around an area. The question asks for how many miles to walk around the property, but it also states the circumference (how many miles around the property) of the property as 1/2 mile. So the area doesn't appear to enter into it.
If the property consists of a circle and a rectangular patch of ground with a total area of 9 acres, I think we may find an answer. The circumference of a circle is 2(pi)r, where r is the radius, so r=880/(2(pi)) yds. The area of the circle is (pi)r^2=(pi)(440/(pi))^2 sq yds = 193600/(pi) sq yds = 61,624.79 sq yds approx. This area exceeds 9 acres, which is only 43,560 sq yds. It now appears that the rectangular patch of ground itself has an area of 9 acres. Let a and b be the sides of the rectangle. If it stands alone, apart from the circle, its perimeter would be 2(a+b) and its area ab=9 acres. Unfortunately we can't find unique values for a and b without more information. We must therefore surmise that a dimension of the rectangle is related to the circle. Perhaps one side of the rectangle has the same length as the diameter of the circle. The shape which comes to my mind is a rectangle with one side removed into which the circle fits. What we have now is a semicircle attached to a rectangle. Let b=880/(pi), the diameter of the circle. Can we can find a? One value would be 9 acres*(pi)/880, but this may not be correct because of the way the circle interacts with the rectangle. The area of the semicircle is 96800/(pi) sq yds = 30,812.40 sq yds. This area is less than 9 acres so it may be that the remaining 12,747.60 sq yds are needed to make up to 43,560 sq yds (9 acres). Let's assume that the rectangle is to have an area of 12,747.60 sq yds, then we can write (880a+96800)/(pi)=43560 (the area of the rectangle plus the area of the semicircle=9 acres=43560 sq yds). From this a=99(pi)/2 - 110 = 45.51 yds.
The total perimeter of the property would then be 2a+b (three sides of the rectangle) + (pi)r (half-circle) = 99(pi)-220+440=531.02 yds=0.302 miles. To walk around the property may require the walker to walk all the way round the circle (880 yds) and then along the three sides of the rectangle. So we need to add a semicircle to this answer making the walk 971.02 yds = 0.552 miles.
If the semicircle is not part of the 9 acre area then we have a different calculation. We need to subtract the area of the semicircle from ab: (880a-96800)/(pi)=43560. From this a=43560(pi)+96800/880=99(pi)/2+110=265.51 yds. And the total perimeter of the property would be 971.02 yds or 1411.02 yds=0.802 miles, depending on whether the walk is just around the perimeter or includes the whole circumference of the circle.
