7. Non-Right Triangles

Which of the following formulas could be used to calculate the area of a sector in a circle with radius $r$ and central angle $\theta$ (in radians)?

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

Which of the following formulas correctly gives the perimeter of a parallelogram with side lengths $a$ and $b$?

What is the sum of the interior angles of a $pentagon$?

Given triangle QRS with sides $q$ and $r$ enclosing angle $S$, what is the formula for the area of triangle QRS?

Given a regular pentagon with a radius (distance from center to a vertex) of $11$ meters, what is the length of its apothem (the perpendicular distance from the center to a side)?

A triangle ABC has sides $a$ and $b$ with included angle $C$. If a sector of a circle with radius $r$ and central angle $C$ is drawn such that the triangle is inscribed within the sector and the region outside the triangle but inside the sector is shaded, what is the area of the sector that is not shaded?

Given a circle with a radius of $12$ units and a central angle of $120°$, what is the area of the sector that is not shaded if the shaded sector corresponds to the given central angle? Choose the closest value.

Given the polar curves $r=3\sin \left(\theta \right)$ and $r=3\cos \left(\theta \right)$, what is the area of the region that lies inside both curves?

Given the polar curves $r^2=18\cdot \sin \left(2\theta \right)$ and $r=3$, what is the area of the region that lies inside both curves?

Given the polar curves $r=7 \sin \left(\theta \right)$ and $r=7 \cos \left(\theta \right)$, what is the area of the region that lies inside both curves?

What is the area of a sector of a circle with a central angle of $90°$ and a radius of $1$ foot?

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?

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

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?