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Let's go through the problems shown in the image and solve them step by step.

### **Problem 1: Perimeter of the Figure**

The first problem asks for the perimeter of the given figure, which is a composite shape made up of rectangles.

1. **Identify the sides:**
   - The sides of the figure are given as: 
     - Horizontal sides: \(4 \, \text{cm}, 2 \, \text{cm}, 3 \, \text{cm}\)
     - Vertical sides: \(2 \, \text{cm}, 3 \, \text{cm}\)

2. **Calculate the perimeter:**
   - Perimeter is the sum of all the outer sides of the figure.

   The perimeter \( P \) is calculated as:
   \[
   P = 4 \, \text{cm} + 2 \, \text{cm} + 2 \, \text{cm} + 3 \, \text{cm} + 3 \, \text{cm} + 3 \, \text{cm} = 17 \, \text{cm}
   \]

   **Solution:** The perimeter of the figure is \(17 \, \text{cm}\).

### **Problem 2: Area of the Figure**

The second problem involves determining the area of a figure composed of different shapes.

1. **Decompose the figure into simpler shapes:**
   - The figure can be decomposed into a rectangle (A1) and a trapezoid (A2).

2. **Calculate the area of each part:**
   - **Area of the Rectangle (A1):**
     - Base \(= 8 \, \text{cm}\)
     - Height \(= 4 \, \text{cm}\)
     \[
     A1 = 8 \, \text{cm} \times 4 \, \text{cm} = 32 \, \text{cm}^2
     \]
   - **Area of the Trapezoid (A2):**
     - Bases: \(8 \, \text{cm}\) and \(4 \, \text{cm}\)
     - Height \(= 3 \, \text{cm}\)
     \[
     A2 = \frac{1}{2} \times (8 \, \text{cm} + 4 \, \text{cm}) \times 3 \, \text{cm} = \frac{1}{2} \times 12 \, \text{cm} \times 3 \, \text{cm} = 18 \, \text{cm}^2
     \]

3. **Sum the areas to find the total area:**
   \[
   \text{Total Area} = A1 + A2 = 32 \, \text{cm}^2 + 18 \, \text{cm}^2 = 50 \, \text{cm}^2
   \]

   **Solution:** The total area of the figure is \(50 \, \text{cm}^2\).

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Would you like more details or have any questions about these solutions? Here are some related questions for further practice:

1. How would the perimeter change if one of the vertical sides was increased by 2 cm?
2. How do you calculate the area of a figure if one of the shapes is a circle?
3. What is the perimeter of a similar figure where each dimension is doubled?
4. How does the area of the trapezoid change if the height is halved?
5. Can you describe how the shape would look if the trapezoid were replaced by a triangle?

**Tip:** When dealing with composite figures, breaking them down into simpler shapes like rectangles, triangles, and trapezoids makes calculating area and perimeter much easier.

Explore how to solve perimeter and area problems of composite figures step-by-step. This page covers calculations involving rectangles, trapezoids, and composite shapes. Suitable for students in Grades 6-8.

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