7. Non-Right Triangles

What is the area of a regular octagon inscribed in a circle of radius $r=6$ meters?

Given the polar curve $r=4+3\cdot \sin \theta$, what is the area enclosed by one complete loop of the curve?

How many sides does a polygon have if the sum of its interior angles is $1440°$?

Given the polar curves $r=5\sin \left(\theta \right)$ and $r=5\cos \left(\theta \right)$, what is the area of the region that lies inside both curves?

A sector of a circle is a region within a circle bounded by two $radii$ and their intercepted arc.

Given a triangle with sides $a$ and $b$ and included angle $C$, which formula correctly gives the area of the triangle using the SAS (Side-Angle-Side) method?

Given the polar curve $r=4+3-\sin \left(\theta \right)$, what is the area enclosed by one loop of the curve?

Given the polar curve $r=4\sin \left(5\theta \right)$, what is the area enclosed by one loop of the curve?

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

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?

If the sum of the interior angles of a polygon is $3420°$, how many sides does the polygon have?

Given triangle QRS with sides $q$ = $5$ units, $r$ = $6$ units, and the included angle $\angle \mathrm{QRS}$ = $60°$, what is the area of triangle QRS?

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?

What is the area of a triangle with side lengths $30$, $40$, and $50$?