step 1
Find out the area of the complete pie
[tex]A=pi*r^2[/tex]r=30/2=15 ft ----> the radius is half the diameter
substitute
[tex]\begin{gathered} A=pi*15^2 \\ A=225pi\text{ ft}^2 \end{gathered}[/tex]Remember that the area of a complete circle, subtends a central angle of 360 degrees
so
Applying proportion
Find out the area for a central angle of 42 degrees
[tex]\begin{gathered} \frac{225pi}{360^o}=\frac{x}{42^o} \\ \\ x=\frac{225p\imaginaryI}{360^{o}}*42^o \\ \\ x=26.25pi \\ x=26.25*3.14 \\ x=82.43\text{ ft}^2 \end{gathered}[/tex]