To find the area and perimeter of shapes $A$ and $B$ from the image you provided, we'll break each shape down into basic components (rectangles and smaller regions). Let's go step by step for both.

Shape A:

Shape $A$ resembles a combination of rectangles.

1. Area of Shape A:

• The upper part is a rectangle with a width of 5 and a height of 2. $\text{Area of top rectangle} = 5 \times 2 = 10$
• The lower part is composed of two vertical strips (with width 1 and height 1 each), and a small horizontal rectangle of width 1 and height 1. $\text{Area of small rectangle in bottom middle} = 1 \times 1 = 1$ $\text{Total area of Shape A} = 10 + 1 = 11$

2. Perimeter of Shape A:

• The perimeter includes the sum of all outer sides. Starting from the top-left corner and moving clockwise: $5 + 2 + 1 + 1 + 1 + 1 + 1 + 2 = 14$ So, the perimeter of shape $A$ is 14 units.

Shape B:

Shape $B$ also resembles a combination of rectangles but with slightly different dimensions than shape $A$.

1. Area of Shape B:

• The upper part is a rectangle with a width of 5 and a height of 2. $\text{Area of top rectangle} = 5 \times 2 = 10$
• The lower part includes two vertical strips (3 units tall and 1 unit wide) and a small square in the middle of size 1 by 1. $\text{Area of small rectangle in bottom middle} = 1 \times 1 = 1$ $\text{Total area of Shape B} = 10 + 1 = 11$

2. Perimeter of Shape B:

• Again, moving clockwise from the top-left corner: $5 + 2 + 1 + 1 + 1 + 1 + 1 + 2 = 14$ So, the perimeter of shape $B$ is also 14 units.

Final Summary:

• Area of Shape A: 11 square units
• Perimeter of Shape A: 14 units
• Area of Shape B: 11 square units
• Perimeter of Shape B: 14 units

Would you like more details or have any further questions? Here are five questions to expand on this topic:

1. What if the dimensions were scaled by a factor of 2—how would that affect the area and perimeter?
2. Can you calculate the area and perimeter of shapes with curved edges?
3. How can you apply this method to find the area of a more complex shape?
4. Could we generalize this approach to composite 3D shapes, like prisms?
5. What is the relationship between the perimeter and area in rectangles?

Tip: The perimeter is always a linear measure, so any changes in dimensions are directly proportional to it, while the area, being two-dimensional, changes quadratically when the dimensions change.