https://file.aiquickdraw.com/mathbot/file/17273448681660e8bxj47.jpg

To calculate the perimeter of this shape, we are dealing with a sector of a circle with a radius of 5 cm and an angle of 120°.

The perimeter of a sector consists of two parts:
1. The length of the curved arc.
2. The two straight sides (which are the radii of the circle).

Let's break this down:

### Step 1: Calculate the arc length.
The formula for the arc length \( L \) of a sector is given by:
\[
L = 2 \pi r \times \frac{\theta}{360^\circ}
\]
where:
- \( r \) is the radius of the circle (5 cm),
- \( \theta \) is the central angle (120°),
- \( \pi \approx 3.1416 \).

Substituting the values:
\[
L = 2 \times 3.1416 \times 5 \times \frac{120}{360}
\]
\[
L = 10 \times 3.1416 \times \frac{1}{3}
\]
\[
L \approx 10.472 \, \text{cm}
\]

### Step 2: Add the lengths of the radii.
The two radii each measure 5 cm, so the total for the straight sides is:
\[
2 \times 5 = 10 \, \text{cm}
\]

### Step 3: Calculate the total perimeter.
Now, adding the arc length and the two radii:
\[
\text{Perimeter} = 10.472 + 10 = 20.47 \, \text{cm}
\]

Thus, the perimeter of the sector is approximately **20.47 cm**.

Would you like more details, or do you have any other questions?

Here are 5 related questions you might explore:
1. How does the perimeter of the sector change if the radius is doubled?
2. What is the area of this sector?
3. How would you calculate the perimeter for a sector with an angle of 90°?
4. What if the radius was 10 cm but the angle remained 120°? What would be the new perimeter?
5. Can you derive the formula for the perimeter of a sector in terms of \( r \) and \( \theta \)?

**Tip:** Always break down complex shapes into simpler components (straight lines, curves) to calculate perimeter or area easily.

Calculate the perimeter of the following shape (a sector with an angle of 120 degrees and a radius of 5 cm).

Learn how to calculate the perimeter of a sector with a 120° angle and a 5 cm radius. This problem explores key geometric concepts including arc length and sector perimeter calculation, suitable for students in Grades 8-10.

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