To find the perimeter of this compound shape, we need to consider the shape's individual components. The given shape is a combination of a rectangle and a semicircle.

Step-by-Step Solution:

1. Identify the components:

   • Rectangle:
     • Length = 20 cm
     • Width = 10 cm
   • Semicircle:
     • The semicircle is attached to one of the shorter sides of the rectangle, so its diameter is equal to the width of the rectangle (10 cm).

2. Calculate the perimeter of the rectangle:

   • Only three sides of the rectangle will contribute to the perimeter because the fourth side is the diameter of the semicircle.
   • Therefore, the perimeter of the three sides of the rectangle is: $P_{\text{rectangle}} = 20 + 10 + 20 = 50 \, \text{cm}$

3. Calculate the perimeter of the semicircle:

   • The perimeter of a full circle is given by $C = \pi \times \text{diameter}$.
   • For a semicircle, the perimeter is half of the full circle's circumference plus the diameter.
   • Diameter of the semicircle = 10 cm.
   • So, the curved part of the semicircle is: $P_{\text{semicircle (curved part)}} = \frac{\pi \times 10}{2} = \frac{3.14 \times 10}{2} = 15.7 \, \text{cm}$
   • Note that the diameter (10 cm) is already included in the perimeter of the rectangle, so we only add the curved part.

4. Calculate the total perimeter of the compound shape: $P_{\text{total}} = P_{\text{rectangle}} + P_{\text{semicircle (curved part)}} = 50 + 15.7 = 65.7 \, \text{cm}$

Final Answer:

The perimeter of the compound shape is 65.7 cm.

Would you like more details or have any questions about this solution?

Related Questions:

1. What is the area of this compound shape?
2. How do we calculate the perimeter of other shapes, such as a quarter circle attached to a rectangle?
3. What would be the perimeter if the semicircle was a full circle?
4. How does the value of $\pi$ affect the calculation of the semicircle’s perimeter?
5. How do we handle similar problems involving different geometric shapes?

Tip:

When dealing with compound shapes, always break them down into simpler shapes and calculate each part separately before combining the results.