Which triangle's area can be calculated using the trigonometric area formula $A=\frac{1}{2}absinC$?

Which formula is used to find the area of a triangle when two sides and the included angle are known (SAS case)?

Given triangle DEF with sides $d$ and $e$ and included angle $F$, what is the formula for its area?

Given a triangle with an included angle of $30°$ and a side of length $7$ feet adjacent to the angle, if the area of the triangle is $12.6$ square feet, what is the length of the base adjacent to the angle?

Given that the measure of central angle $\mathrm{QRS}$ is $\theta$ radians in a circle of radius $r$, what is the area of the shaded sector? Choose the correct formula from the options below.

Given a circle with radius $8$ units and a central angle $\theta$ measuring $\frac{2}{3}$ radians, what is the area of the shaded sector?

Given a circle with radius $r$ and a central angle $\theta$ measured in radians, what is the area of the shaded sector formed by this angle?

What is the area of a rectangle that is $11$ units long and $5$ units wide?