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Given the following composite figure, d = 6.4 cm and w = 19.5 cm.

 

What is the perimeter of the figure?

 

Composite Figure

 

Use 3.14 for pi, and round your answer to the nearest hundredth. Do not include "cm" with your response.

 

The composite figure in the image appears to be a capsule shape, consisting of a rectangle in the middle and two semicircles on either end. To find the perimeter of this figure, we need to calculate the perimeter of both the rectangle and the semicircles.

### Given dataThe composite figure in the image appears to be a capsule shape, consisting of a rectangle in the middle and two semicircles on either end. To find the perimeter of this figure, we need to calculate the perimeter of both the rectangle and the semicircles.

### Given 
- \( d = 6.4 \, \text{cm} \) (this is the diameter of the semicircles, so the radius \( r = \frac{d}{2} = 3.2 \, \text{cm} \)).
- \( w = 19.5 \, \text{cm} \) (this is the total width of the figure, which includes the length of the rectangle and the two semicircles).

### Steps to calculate the perimeter:

1. **Perimeter of the semicircles**:
   - Two semicircles make a full circle.
   - The circumference of a circle is \( C = \pi d \).
   - Therefore, the perimeter of the two semicircles is:
   \[
   P_{\text{semicircles}} = \pi d = 3.14 \times 6.4 = 20.096 \, \text{cm}
   \]

2. **Length of the rectangle**:
   - The total width \( w = 19.5 \, \text{cm} \) includes the diameter of both semicircles.
   - So, the length of the rectangle \( L_{\text{rect}} = w - d = 19.5 - 6.4 = 13.1 \, \text{cm} \).

3. **Perimeter of the rectangle (along its two lengths)**:
   - The rectangle contributes twice its length to the perimeter:
   \[
   P_{\text{rect}} = 2 \times 13.1 = 26.2 \, \text{cm}
   \]

4. **Total perimeter**:
   - The total perimeter is the sum of the perimeter of the semicircles and the rectangle:
   \[
   P_{\text{total}} = P_{\text{semicircles}} + P_{\text{rect}} = 20.096 + 26.2 = 46.296 \, \text{cm}
   \]

### Rounded to the nearest hundredth:
\[
P_{\text{total}} \approx 46.30
\]

Thus, the perimeter of the figure is **46.30**.

Would you like more details or have any other questions?

Here are 5 related questions:
1. How would the perimeter change if the diameter \( d \) were increased by 2 cm?
2. What is the area of this composite figure?
3. If the radius was doubled, what would the new perimeter be?
4. How does changing the value of \( \pi \) from 3.14 to 3.14159 affect the perimeter?
5. How do we calculate the perimeter of a rectangle alone?

**Tip:** In capsule shapes, the perimeter involves calculating both circular and linear sections—always separate them for better clarity!

Given the following composite figure, d = 6.4 cm and w = 19.5 cm. What is the perimeter of the figure? Use 3.14 for pi, and round your answer to the nearest hundredth. Do not include 'cm' with your response.

Learn how to calculate the perimeter of a capsule-shaped composite figure using given dimensions. This problem involves geometry concepts such as the circumference of circles and perimeter of rectangles. Suitable for students in Grades 7-9.

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