The area of a sector with central angle θ and radius r is:

\(A=θ/360°×πr^2\)

Since the measure of an arc is equal to the measure of its central angle, we know that \(θ=x=80°\). Given r=12 cm, we have

\(A=80°/360°×π(12)^2\)

\(A=2/9×144π\)

\(A=32π sq. cm\)