https://r2.erweima.ai/mathbot/image/1725904620000rf2yrfrs.jpg

To find the area of the polygon in the image, we can decompose it into simpler shapes. From the image, the polygon can be broken down into two triangles and one rectangle, or into two triangles and a trapezoid. Let’s analyze both approaches.

### Step 1: Analyze the Shape
- The polygon is a trapezoid because it has one pair of parallel sides (top and bottom).
- The grid provided helps us determine the dimensions easily.

### Step 2: Decomposition and Calculation
Using the grid, we count:
- The **top side** (parallel side): 4 units.
- The **bottom side** (parallel side): 8 units.
- The **height** (vertical distance between the parallel sides): 3 units.

### Step 3: Use the Trapezoid Area Formula
The formula for the area of a trapezoid is:

\[
\text{Area of trapezoid} = \frac{1}{2} \times (b_1 + b_2) \times h
\]

Where:
- \(b_1\) is the length of the top side (4 units),
- \(b_2\) is the length of the bottom side (8 units),
- \(h\) is the height (3 units).

Substitute the values into the formula:

\[
\text{Area} = \frac{1}{2} \times (4 + 8) \times 3 = \frac{1}{2} \times 12 \times 3 = 18 \, \text{square units}
\]

### Conclusion:
The area of the polygon is **18 square units**.

Would you like more details on this process or a different approach to solving it? 

Here are some related questions you could explore:
1. How do you calculate the area of irregular polygons?
2. What is the difference between decomposing shapes and using formulas directly?
3. How do you calculate the area of a polygon using triangles?
4. Can you apply the Pythagorean theorem to solve area problems?
5. How does the concept of base and height apply to parallelograms versus trapezoids?

**Tip:** When decomposing complex polygons, use the properties of known shapes like triangles, rectangles, and trapezoids for easier calculations.

Find the area of the polygon shown in the grid. You can think of it as two triangles or a rectangle and two triangles.

Learn how to calculate the area of a polygon by decomposing it into simpler shapes like triangles and rectangles. This problem demonstrates using the trapezoid area formula with step-by-step calculations. Suitable for Grades 6-8.

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