To solve for the area of the shaded polygon, which has been decomposed into two triangles, let's analyze each triangle and add their areas.

Step-by-Step Solution:

1. Identify the Base and Height of Each Triangle:

   • Observing the grid, the shaded polygon is split into two triangles by the dotted line in the center.
   • We will calculate the area of each triangle separately and then add them together.

2. Top Triangle:

   • Base: The top triangle's base spans across 4 units (as seen horizontally on the grid).
   • Height: The height of this triangle is 3 units (from the dotted line to the top vertex of the triangle).
   • Area of the top triangle = $\frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 4 \times 3 = 6$ square units.

3. Bottom Triangle:

   • Base: The bottom triangle also has a base of 4 units (across the dotted line).
   • Height: The height of the bottom triangle is also 3 units (from the dotted line to the bottom vertex of the triangle).
   • Area of the bottom triangle = $\frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 4 \times 3 = 6$ square units.

4. Total Area of the Polygon:

   • Adding the areas of both triangles gives us $6 + 6 = 12$ square units.

Answer:

The total area of the shaded polygon is 12 square units.

Would you like more details on any of these steps or have any questions?

Additional Related Questions:

1. How would the area change if the height of each triangle increased by 1 unit?
2. What is the perimeter of the shaded polygon?
3. How would you calculate the area if the polygon was divided differently?
4. Can you decompose any polygon into triangles to find its area?
5. What would be the area if the base of each triangle was reduced by 1 unit?

Tip:

When calculating the area of a polygon decomposed into triangles, always check if the triangles share the same base and height, as this can simplify calculations.