To find the area and perimeter of the given shape, let's first analyze the shape and break it down into simpler geometric figures.

1. Analyzing the Shape:

The given shape can be split into two rectangles:

• Rectangle 1: The bottom rectangle has dimensions 6 cm (width) and 5 cm (height).
• Rectangle 2: The top-right rectangle has dimensions 4 cm (width) and 3 cm (height). This height is determined by subtracting the height of the bottom rectangle (5 cm) from the total height of the shape (8 cm).

2. Calculating the Area:

To find the total area of the shape, we sum the areas of the two rectangles.

• Area of Rectangle 1: $\text{Area}_1 = \text{width} \times \text{height} = 6 \, \text{cm} \times 5 \, \text{cm} = 30 \, \text{cm}^2$

• Area of Rectangle 2: $\text{Area}_2 = \text{width} \times \text{height} = 4 \, \text{cm} \times 3 \, \text{cm} = 12 \, \text{cm}^2$

• Total Area: $\text{Total Area} = \text{Area}_1 + \text{Area}_2 = 30 \, \text{cm}^2 + 12 \, \text{cm}^2 = 42 \, \text{cm}^2$

3. Calculating the Perimeter:

To find the perimeter, we need to sum up the lengths of all the sides of the shape.

• The perimeter includes:
  • Bottom side of Rectangle 1: 6 cm
  • Left side of Rectangle 1: 5 cm
  • Left side of Rectangle 2 (which is vertical from the bottom left to top left of the shape): 3 cm
  • Top side of Rectangle 2: 4 cm
  • Right side of Rectangle 2 (total height of the shape): 8 cm
  • The small side between the top of Rectangle 1 and bottom of Rectangle 2: 2 cm (total width - width of rectangle 2, i.e., 6 - 4)

So, the perimeter $P$ is calculated as: $P = 6 + 5 + 3 + 4 + 8 + 2 = 28 \, \text{cm}$

4. Final Answers:

• Area: $42 \, \text{cm}^2$
• Perimeter: $28 \, \text{cm}$

Would you like more details, or do you have any other questions?

Here are some related questions that might interest you:

1. How do you find the area of composite shapes?
2. What is the formula for finding the perimeter of irregular shapes?
3. Can you explain how to find the area of a shape with more complex geometry?
4. How do you calculate the perimeter if some sides are unknown?
5. How do you convert the area from square centimeters to square meters?

Tip: When solving geometry problems, breaking down complex shapes into simpler parts (like rectangles or triangles) can simplify the calculations.