To find the perimeter of the given shape, let's break down the problem.

The shape consists of a rectangle and two semicircles (one added and one subtracted).

Steps to Calculate the Perimeter:

1. Identify the dimensions of the rectangle:

   • Height = 4 inches
   • Length = 4 inches

2. Perimeter of the rectangle: $P_{\text{rectangle}} = 2 \times (\text{Height} + \text{Length}) = 2 \times (4 + 4) = 16 \text{ inches}$

3. Circumference of a full circle with diameter 4 inches:

   • Radius = $\frac{4}{2} = 2 \text{ inches}$
   • Circumference of a full circle = $2\pi \times \text{Radius} = 2\pi \times 2 = 4\pi \text{ inches}$

4. Circumference of one semicircle: $C_{\text{semicircle}} = \frac{4\pi}{2} = 2\pi \text{ inches}$

5. Add the lengths of the semicircles to the perimeter:

   • Since the shape has one semicircle subtracted and another added, the perimeter contributions of the semicircles cancel each other out in terms of net length.
   • Therefore, only the straight edges of the semicircle contribute to the overall perimeter.

6. Total Perimeter Calculation:

   • The straight edges of the semicircle on the right (removed part) do not contribute to the perimeter, but the remaining perimeter includes the curved part of the left semicircle and the sides of the rectangle.

Thus, the final perimeter includes:

• The three sides of the rectangle (one side is replaced by the curved semicircle edge):
  • Two vertical sides (2 × 4 inches) = 8 inches
  • One horizontal side (4 inches)
• Plus the curved part of the semicircle (2π inches)

So, the final perimeter $P$ is: $P = 8 + 4 + 2\pi \approx 12 + 6.28 = 18.28 \text{ inches}$

Therefore, the perimeter of the shape is approximately 18.28 inches.

Would you like more details or have any questions?

Related Questions:

1. What is the area of the given shape?
2. How would the perimeter change if the semicircles had a different diameter?
3. How do you find the circumference of a semicircle?
4. Can you derive the formula for the perimeter of a semicircular shape?
5. What would be the perimeter if the rectangle's dimensions were different?
6. How do you calculate the area of a semicircle?
7. What is the significance of π in circle-related calculations?
8. How do the properties of circles and rectangles interact in composite shapes?

Tip:

Always remember to break down composite shapes into simpler components to calculate their perimeter or area more easily.