Chapter 13, Trigonometric Ratios and Functions - 13.2 Define General Angles and Use Radian Measure - 13.2 Exercises - Skill Practice - Page 863: 38

$12.57cm^2$

We know the following: $$A=\dfrac{1}{2} r^2\theta$$ Here, $40^{\circ}=(40^{\circ}) \times ( \dfrac{ \pi\ radians}{180^{\circ}})=\dfrac{2 \pi}{9} radians$ Here, $\theta$ is in radians. Thus: $$A=(\dfrac{1}{2})(6)^2\times( \dfrac{ 2\pi}{9}) \approx 12.57cm^2$$