Sector A has a radius of $5 \text{ units}$ and a central angle of $2 \text{ radians}$. Sector B has a radius of $10 \text{ units}$ and a central angle of $1 \text{ radian}$. Which of the following statements is true regarding their areas?

True or False: The area of a segment is always less than the area of the sector formed by the same arc and radii.

A sector of a circle has a radius of ${6 ext{ cm}}$ and an arc length of ${4 ext{ cm}}$. Calculate the area of the sector.

A windshield wiper is $40\text{ cm}$ long and rotates through an angle of $150^{\circ}$. Calculate the area of the windshield swept by the wiper.

A circle has a radius $r = 8 \text{ cm}$. A chord subtends a central angle of $\theta = 90^{\circ}$. Calculate the length of the chord .