To determine the area of the given shape, let's analyze it step by step.

Step 1: Break the shape into components

The shape consists of:

1. A rectangular section at the bottom with:

   • Width = $21 \, \text{cm}$
   • Height = $16 \, \text{cm}$

2. A triangular section at the top with:

   • Base = $21 \, \text{cm}$ (same as the width of the rectangle)
   • Height = $32 - 16 = 16 \, \text{cm}$ (difference between the total height and the rectangle's height)

Step 2: Calculate the area of each section

1. Rectangle Area: $\text{Area}_{\text{rectangle}} = \text{width} \times \text{height} = 21 \times 16 = 336 \, \text{cm}^2$

2. Triangle Area: $\text{Area}_{\text{triangle}} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 21 \times 16 = 168 \, \text{cm}^2$

Step 3: Total Area

$\text{Total Area} = \text{Area}_{\text{rectangle}} + \text{Area}_{\text{triangle}} = 336 + 168 = 504 \, \text{cm}^2$

Final Answer:

The area of the shape is $504 \, \text{cm}^2$.

Would you like me to expand on any part of the process? Here are some related questions:

1. How do you determine the base or height of a shape in composite figures?
2. What is the general formula for the area of a triangle?
3. Why is breaking composite shapes into basic ones important?
4. Can this method work for irregular polygons? How?
5. What are other shapes commonly broken into rectangles and triangles?

Tip: Always ensure to subtract overlapping areas if two shapes intersect in composite figures!