The image shows a polygon that has been decomposed into two triangles, and you're asked to find the total area of the shaded polygon. The polygon is on a grid, and we can use the geometry of the triangles to find the solution.

Let's break this down:

1. Identify the triangles: The polygon is made up of two right triangles, each with a clear base and height, as they align with the grid.

2. Area of a triangle formula: The area of a triangle is given by the formula: $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$

   We need to calculate the area of each triangle and add them together to get the total area of the polygon.

Steps to calculate:

• Triangle 1: From the grid, this triangle seems to have a base of 4 units and a height of 2 units. $\text{Area of Triangle 1} = \frac{1}{2} \times 4 \times 2 = 4 \, \text{square units}$

• Triangle 2: This triangle seems to have a base of 3 units and a height of 4 units. $\text{Area of Triangle 2} = \frac{1}{2} \times 3 \times 4 = 6 \, \text{square units}$

Total Area:

$\text{Total Area} = 4 + 6 = 10 \, \text{square units}$

Thus, the total area of the shaded polygon is 10 square units.

Let me know if you need further clarification or details!

Here are some related questions to deepen your understanding:

1. How do you calculate the area of irregular polygons?
2. What happens if the triangles in the polygon aren't right triangles?
3. How can you verify the area using another method, like counting grid squares?
4. How would the area formula change if the triangles were scalene?
5. How can you apply the area formula to real-world objects?

Tip: When decomposing shapes into triangles, always check if the triangles are right triangles—it simplifies the calculations!