To find the area of the shaded polygon, we need to approach the problem by breaking down the shape into simpler geometric components. The polygon appears to be a large triangle with a small rectangle subtracted from it. Let's calculate the area step-by-step:

1. Calculate the area of the large triangle:

   • The base of the triangle is $14$ cm.
   • The height of the triangle is $5$ cm (3 cm + 2 cm, from the figure).

   The area of a triangle is given by: $\text{Area of triangle} = \frac{1}{2} \times \text{base} \times \text{height}$ Substituting the values: $\text{Area of triangle} = \frac{1}{2} \times 14 \times 5 = 35 \text{ cm}^2$

2. Calculate the area of the small rectangle:

   • The width of the rectangle is $2$ cm.
   • The height of the rectangle is $2$ cm.

   The area of a rectangle is given by: $\text{Area of rectangle} = \text{width} \times \text{height}$ Substituting the values: $\text{Area of rectangle} = 2 \times 2 = 4 \text{ cm}^2$

3. Calculate the area of the shaded region:

   The shaded area is the area of the large triangle minus the area of the small rectangle. $\text{Shaded area} = 35 - 4 = 31 \text{ cm}^2$

So, the area of the shaded polygon is $31 \text{ cm}^2$.

Would you like a more detailed explanation or have any questions?

Here are some related questions to further explore the concept:

1. How would the area change if the height of the rectangle was increased by 1 cm?
2. What is the perimeter of the shaded polygon?
3. How would you find the centroid of the shaded polygon?
4. What if the large triangle had an isosceles or scalene shape, how would that affect the calculation?
5. How would the shaded area be affected if the base of the large triangle was decreased by 2 cm?

Tip: Always break down complex shapes into simpler geometric components for easier calculation of areas and perimeters.