What is the area of a sector with a central angle of 2π/9 radians and a radius of 16.7 ft?

First, we determine the area of the whole circle that can be calculated through the equation,

A = πr²

Substituting,

A = π (16.7 ft) ² = 278.89π ft²

Then, we multiply the area obtained by the ratio of the given angle to the whole revolution.

Area of the sector = ((2π/9) / 2π) x 278.89π ft²

= 30.99π ft²

Thus, the area of the sector is approximately 30.99π ft².