Before it is cut, you have a circle with diameter 6ft which means it had a radius of 3ft
After it is cut, you now have a semi-circle still with diameter 6ft and radius 3ft
[tex]Area \: of a \: circle = \pi {r}^{2} [/tex]
[tex]Area \: of a \: semi-circle = \frac{\pi {r}^{2} }{2} [/tex]
Substitute the values you have
[tex] Area = \frac{\pi \times {3}^{2} }{2} [/tex]
Area = 14.14ft squared