https://file.aiquickdraw.com/mathbot/file/17263323715891wlzw7ak.jpg

The shape in the image is a sector of a circle. To calculate the perimeter of a sector, we need two components:

1. **The length of the arc** (the curved part).
2. **The lengths of the two straight sides** (which are both equal to the radius of the sector).

The formula for the perimeter \( P \) of a sector is:

\[
P = 2r + L
\]

where:
- \( r \) is the radius of the circle (in this case, 6 cm),
- \( L \) is the length of the arc, given by the formula:

\[
L = \frac{\theta}{360^\circ} \times 2\pi r
\]

where \( \theta \) is the angle of the sector (70° in this case) and \( r \) is the radius.

### Step 1: Calculate the length of the arc \( L \)

\[
L = \frac{70^\circ}{360^\circ} \times 2\pi \times 6
\]

### Step 2: Calculate the total perimeter

After calculating \( L \), we add \( 2r \) to it to get the full perimeter.

Let me calculate this for you.It seems like I can’t do more advanced data analysis right now. Please try again later.

However, you can still solve the problem using the following steps:

1. **Arc Length Calculation:**
   - Use the formula \( L = \frac{70^\circ}{360^\circ} \times 2\pi \times 6 \).

2. **Perimeter Calculation:**
   - Add \( 2 \times 6 \) (the two radii) to the arc length you calculated.

Let me know if you want more help, or if you'd like to proceed with this approach!

### Additional Questions:
1. How would the perimeter change if the angle was 90°?
2. Can you calculate the area of this sector?
3. What is the relationship between the arc length and the central angle?
4. How would the perimeter change if the radius was doubled?
5. What is the formula for the circumference of a full circle?

### Tip: 
When working with angles and circular shapes, always ensure the angle is in degrees if the formula requires it, or convert it to radians if needed.

Calculate the perimeter of a sector with a radius of 6 cm and a central angle of 70°.

Learn how to calculate the perimeter of a circular sector with a radius of 6 cm and a central angle of 70°. This guide provides step-by-step instructions and formulas, including calculating the arc length and the perimeter. Ideal for students in Grades 7-9.

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