Let’s calculate the areas and perimeters of the shapes provided:

General Approach:

• Area: Count the number of squares in each shape.
• Perimeter: Add up the lengths of all the exposed edges of the shape. Each square unit has 4 sides, but shared sides between squares don’t count.

a) Shape:

• Area: Count the squares: 5 square units.
• Perimeter: Count exposed edges:
  • Top: 3 units.
  • Left: 3 units.
  • Bottom: 4 units.
  • Right: 4 units.
  • Total perimeter = 3 + 3 + 4 + 4 = 14 units.

b) Shape:

• Area: Count the squares: 6 square units.
• Perimeter: Count exposed edges:
  • Top: 4 units.
  • Left: 3 units.
  • Bottom: 4 units.
  • Right: 4 units.
  • Total perimeter = 4 + 3 + 4 + 4 = 15 units.

c) Shape:

• Area: Count the squares: 7 square units.
• Perimeter: Count exposed edges:
  • Top: 5 units.
  • Left: 3 units.
  • Bottom: 4 units.
  • Right: 4 units.
  • Total perimeter = 5 + 3 + 4 + 4 = 16 units.

d) Shape:

• Area: Count the squares: 8 square units.
• Perimeter: Count exposed edges:
  • Top: 5 units.
  • Left: 3 units.
  • Bottom: 5 units.
  • Right: 5 units.
  • Total perimeter = 5 + 3 + 5 + 5 = 18 units.

e) Next Shape:

To identify the next shape:

• Add one more square to the existing "L" structure to continue the pattern. This will result in a shape with 9 square units.
• Area: 9 square units.
• Perimeter: Likely extends to:
  • Top: 6 units.
  • Left: 3 units.
  • Bottom: 5 units.
  • Right: 5 units.
  • Total perimeter = 6 + 3 + 5 + 5 = 19 units.

Would you like me to explain any part of this in detail or help you visualize the next shape? Here are 5 questions for further exploration:

1. How do you calculate the shared edges in a complex shape's perimeter?
2. Can you identify patterns in the areas and perimeters of this sequence?
3. How might the pattern continue after the next shape?
4. What is the relationship between the number of squares and the perimeter?
5. How could this problem apply to real-world spatial problems?

Tip: Always double-check exposed edges when counting the perimeter to avoid overestimation.