What is the area of a sector with a central angle of 4π/5 radians and a radius of 11 cm?

the area of a sector is 151.976 cm² ...

Step-by-step explanation:

Area of sector (A) is given by:

A=πr².θ/360°

where,

r is the radius and θ is the angle in degree.

As per the statement:

A central angle of 4π/5 radians and a radius of 11 cm.

r=11cm

Use conversion:

1 radian=180/π

then:

4π/5 radians=180/π * 4π/5

=144°

θ=144°

Substitute these given values and use 3.14 for π we have;

A=3.14 * (11) ²*144/360

A=3.14 (121) * 144/360

A=379.94*0.4

A=151.976 cm²

Therefore the area of a sector is 151.976 cm² ...