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The problem in the image involves calculating the perimeter (keliling) of a Pacman-shaped sector that covers \( \frac{5}{6} \) of a full circle with a radius of 1 cm.

### Step-by-step solution:

1. **Given Information:**
   - The sector covers \( \frac{5}{6} \) of the circle.
   - Radius \( r = 1 \, \text{cm} \).

2. **Formula for the perimeter of a sector:**
   The perimeter (keliling) of a sector consists of two parts:
   - The arc length of the sector.
   - The two radii that form the sides of the sector.

   Perimeter = Arc Length + 2 × Radius

3. **Arc Length Calculation:**
   The arc length \( L \) for a sector is given by:
   \[
   L = \theta \times r
   \]
   where \( \theta \) is the central angle in radians. For a full circle, the angle is \( 2\pi \), and since the sector covers \( \frac{5}{6} \) of the circle, the angle of the sector is:
   \[
   \theta = \frac{5}{6} \times 2\pi = \frac{5\pi}{3}
   \]
   So, the arc length is:
   \[
   L = \frac{5\pi}{3} \times 1 = \frac{5\pi}{3}
   \]

4. **Complete Perimeter:**
   Adding the two radii (which are both 1 cm each):
   \[
   \text{Perimeter} = \frac{5\pi}{3} + 2
   \]

Thus, the correct answer is:
\[
\boxed{a. \, \frac{5\pi}{3} + 2}
\]

Would you like more details on any part of the solution? Here are five related questions to extend your understanding:

1. How is the arc length of a sector derived from the angle and radius?
2. What is the formula for the circumference of a full circle?
3. How would the solution change if the sector covered a different fraction of the circle?
4. What is the role of the central angle in determining the arc length?
5. How do we calculate the perimeter if the radius of the circle changes?

**Tip:** Always ensure to include both the arc length and the two radii when calculating the perimeter of a sector!

Dalam game arcade, monster Pacman berbentuk juring 5/6 putaran dari suatu lingkaran yang berjari-jari 1 cm. Keliling dari tubuh monster tersebut adalah ... cm.

This problem involves calculating the perimeter of a sector that forms 5/6 of a full circle with a radius of 1 cm. Learn how to apply the arc length formula and sector perimeter formula. Suitable for students in Grades 8-10.

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