To find the area of the shaded region, let’s go through the information provided and the relevant geometry.

1. Given Data:

   • $\angle C = \angle D = 90^\circ$
   • $\angle B = 60^\circ$
   • $AP = 3 \, \text{cm}$

2. Analysis of the Shape:

   • The shape is a quadrilateral, and $\angle B$ at 60° implies that triangle $ABP$ (the shaded area) is an equilateral triangle since $\angle B = 60^\circ$ and two sides are equal (isosceles property).

3. Calculating Area of the Equilateral Triangle (Shaded Region):

   • For an equilateral triangle with side length $s = 3 \, \text{cm}$, the area $A$ is given by: $A = \frac{\sqrt{3}}{4} s^2$ Substituting $s = 3 \, \text{cm}$: $A = \frac{\sqrt{3}}{4} \times 3^2 = \frac{\sqrt{3}}{4} \times 9 = \frac{9\sqrt{3}}{4} \, \text{cm}^2$

4. Comparing Options:

   • The area does not directly match any options since the options are given in terms of $\pi$ rather than $\sqrt{3}$.

5. Re-evaluation of Approach (If Required):

   • The question might imply a specific interpretation, but based on the details given, this is the most straightforward calculation.

Would you like further details on this solution or have any other questions?

1. How is the area of an equilateral triangle calculated?
2. Why is the angle $\angle B = 60^\circ$ significant in identifying the triangle type?
3. How do different units like $\pi$ and $\sqrt{3}$ affect comparisons in areas?
4. What is the general approach to finding shaded regions in geometric figures?
5. How can understanding triangle properties simplify complex geometry problems?

Tip: Always verify if shapes follow standard properties (like angles in triangles) to simplify calculations.