half the diameter is the radius, so
[tex]r=15[/tex]now we can calculate the total area of the circle , and then will calculate the area for the angle
[tex]\begin{gathered} A=\pi\times r^2 \\ A=\pi\times15^2 \\ A=225\pi \end{gathered}[/tex]the area of the circle is 225pi, this is the corresponding area for the complete angle of the circle, therefore it is equivalent to 2pi
now we create a relation to find the area corresponding to the indicated angle
if 225pi is equal to 2pi how much is 3pi / 5
[tex]\begin{gathered} 225\pi\longrightarrow2\pi \\ x\longrightarrow\frac{3}{5}\pi \end{gathered}[/tex]where x is the area covered by the angle
we solve ussing cross multiplication, x is equal to: multiply the values that are found diagonally and make them equal
[tex]\begin{gathered} x\times2\pi=\frac{3}{5}\pi\times225\pi \\ \end{gathered}[/tex]and solve for x
[tex]\begin{gathered} x=\frac{\frac{3}{5}\pi\times225\pi}{2\pi} \\ \\ x=\frac{135\pi^2}{2\pi} \\ \\ x=67.5\pi\approx212.0575 \end{gathered}[/tex]The rounded area is 212.0575 square feet
