Question

The measure of central angle ABC is radians. What is the area of the shaded sector?

Answer 1

it seems your question is incomplete. A complete question is attached in figure as shown below.

we know, area of sector is given by
$A=\frac{\theta}{360^{\theta}}\pi r^2$

if $\theta$ is in radian,
then, A = $\frac{\theta}{2\pi}\pi r^2$

or, A = $\frac{1}{2}\theta r^2$

Here given,
r = 6 unit
$\angle{ABC}=\theta=\frac{\pi}{2}$

so, A = 1/2 × (6)² × π/2

A = 1/2 × 36 × π/2 = 9π unit²

hence, option (b) is correct.