https://file.aiquickdraw.com/mathbot/file/1729213558756bh7rzf28.jpg

The image shows a sector of a circle with a central angle \(\angle EFG = 120^\circ\), and the length of line segment \(EF\) (which is the radius of the circle) is \(24 \, \text{cm}\). You are asked to calculate the perimeter of the shaded area.

### Step-by-step Solution:

#### 1. **Identify the elements of the sector:**
   - Radius \(r = 24 \, \text{cm}\)
   - Central angle \(\theta = 120^\circ\)

#### 2. **Arc Length Calculation:**
   The formula for the length of an arc \(L\) in a sector is:
   \[
   L = 2\pi r \times \frac{\theta}{360^\circ}
   \]
   Substituting the known values:
   \[
   L = 2\pi \times 24 \times \frac{120}{360} = 48\pi \times \frac{1}{3} = 16\pi \, \text{cm}
   \]
   Approximate this as:
   \[
   L \approx 16 \times 3.14 = 50.24 \, \text{cm}
   \]

#### 3. **Calculate the Perimeter of the Shaded Area:**
   The perimeter of the shaded area includes:
   - The arc length (\(L = 50.24 \, \text{cm}\)),
   - Two radii \(EF = 24 \, \text{cm}\) and \(FG = 24 \, \text{cm}\).

   Thus, the total perimeter \(P\) is:
   \[
   P = L + EF + FG = 50.24 + 24 + 24 = 98.24 \, \text{cm}
   \]

So, the perimeter of the shaded area is approximately **98.24 cm**.

Do you want more details or have any questions?

### Related Questions:
1. How would the perimeter change if the central angle was 90° instead of 120°?
2. Can you calculate the area of the shaded region?
3. What is the length of the circumference of the entire circle?
4. How do we calculate the area of a sector given a different radius?
5. How would the solution differ if the central angle was given in radians?

### Tip:
Always ensure to convert angles into radians when working with formulas involving trigonometric functions.

Hitunglah keliling daerah yang diarsir. Diketahui besar ∠EFG = 120° dan panjang EF = 24 cm.

Learn how to calculate the perimeter of a sector with a central angle of 120° and a radius of 24 cm. This problem involves geometry concepts like arc length and sector perimeter. Suitable for students in Grades 9-10.

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