1. The problem involves finding areas of common shapes given side lengths and angles. 2. For (a) the triangle with sides $p$ and $q$ and included angle $75^\circ$, use the formula for the area of a triangle given two sides and the included angle: $$\text{Area} = \frac{1}{2} p q \sin(75^\circ)$$ This formula comes from the fact that the area equals half the product of two sides times the sine of the included angle. 3. For (b) the quadrilateral with sides $s$ and $r$ and angles $147^\circ$, $38^\circ$, and $125^\circ$, the area calculation depends on more information such as whether it can be divided into triangles or if it is cyclic. Without additional data, the area cannot be determined directly from the given information. 4. For (c) the triangle with angles $62^\circ$, $95^\circ$, and $57^\circ$, if a side length is known, the area can be found using the Law of Sines to find other sides and then the standard area formulas. Without side lengths, the area cannot be computed. Summary: - (a) Area formula: $$\frac{1}{2} p q \sin(75^\circ)$$ - (b) Insufficient data for area calculation. - (c) Insufficient data without side lengths. Hence, the only explicit area formula given the data is for (a).