https://file.aiquickdraw.com/mathbot/file/1728565637165dpjdk2km.jpg

To calculate the area of the given figure, we need to analyze its shape, dimensions, and structure.

### Step 1: Break down the shape
The shape consists of:
- A rectangle in the lower part with a width of \(1 \, \text{cm}\) and height of \(2 \, \text{cm}\).
- A trapezoidal part on the top, where the top length is \(1 \, \text{cm}\) and the bottom length is also \(1 \, \text{cm}\), and the height of the trapezoid is \(1 \, \text{cm}\).

### Step 2: Calculate the area of each part
1. **Rectangle area**:
   \[
   \text{Area of rectangle} = \text{width} \times \text{height} = 1 \, \text{cm} \times 2 \, \text{cm} = 2 \, \text{cm}^2
   \]

2. **Trapezoid area**:
   Since the trapezoid's top and bottom lengths are the same, the area can be treated as the area of a rectangle (as it's essentially a rectangle):
   \[
   \text{Area of trapezoid} = \text{top length} \times \text{height} = 1 \, \text{cm} \times 1 \, \text{cm} = 1 \, \text{cm}^2
   \]

### Step 3: Total area
The total area is the sum of the areas of the rectangle and the trapezoid:
\[
\text{Total area} = 2 \, \text{cm}^2 + 1 \, \text{cm}^2 = 3 \, \text{cm}^2
\]

Thus, the area of the shape is **3 square centimeters**.

Would you like further clarification, or have any questions?

Here are some related questions:
1. How would the area change if the dimensions were doubled?
2. Can this shape be decomposed into different geometric figures for alternative methods of finding the area?
3. How does the perimeter of this shape compare to its area?
4. How can the area formula for a trapezoid be applied in different cases?
5. What is the effect on the area if the height of the trapezoid is increased by 50%?

**Tip:** Always double-check dimensions in composite shapes and their relationships when calculating areas.

This page explains how to calculate the area of a composite shape, combining a rectangle and a trapezoid. The figure has dimensions of 1 cm for the width and height of the rectangle, and 1 cm height for the trapezoid. Step-by-step solution provided for students in Grades 6-8.

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