To solve for the area and perimeter of these two shapes, let's analyze them one by one based on their structure.

Left Shape

1. Perimeter Calculation:

   • The perimeter is the sum of all the side lengths.
   • The lengths are: $5 + 2 + 2 + 2 + 1 + 1 + 1 + 2$.
   • $\text{Perimeter} = 5 + 2 + 2 + 2 + 1 + 1 + 1 + 2 = 16$ units.

2. Area Calculation:

   • Divide the shape into two rectangles.
     • The upper rectangle has a width of 5 and a height of 2.
     • The lower rectangle (cut-out) has a width of 1 and a height of 1.
   • Area of the upper rectangle: $5 \times 2 = 10$ square units.
   • Subtract the area of the lower rectangle: $1 \times 1 = 1$ square unit.
   • Total Area: $10 - 1 = 9$ square units.

Right Shape

1. Perimeter Calculation:

   • The perimeter is the sum of all side lengths.
   • The lengths are: $5 + 2 + 2 + 3 + 1 + 1 + 1 + 1$.
   • $\text{Perimeter} = 5 + 2 + 2 + 3 + 1 + 1 + 1 + 1 = 16$ units.

2. Area Calculation:

   • Divide the shape into two rectangles.
     • The upper rectangle has a width of 5 and a height of 2.
     • The lower rectangle (cut-out) has a width of 1 and a height of 1.
   • Area of the upper rectangle: $5 \times 2 = 10$ square units.
   • Subtract the area of the lower rectangle: $1 \times 1 = 1$ square unit.
   • Total Area: $10 - 1 = 9$ square units.

Summary

• Left Shape: Area = 9 square units, Perimeter = 16 units.
• Right Shape: Area = 9 square units, Perimeter = 16 units.

Would you like further details or explanations?

Related Questions:

1. How would the area change if the bottom cut-out was 2 units wide?
2. Can you find the perimeter if the height of the shape is increased by 1 unit on both sides?
3. What would happen to the area if both the upper and lower rectangles had the same height?
4. How can the perimeter be calculated if the width of the upper rectangle is changed to 6?
5. Is it possible for the two shapes to have different areas if their perimeters remain the same?

Tip:

When calculating the area of composite shapes, break them down into smaller, simpler rectangles or triangles to make the calculation easier.