https://file.aiquickdraw.com/mathbot/file/1726638951501f2nfqz08.jpg

The problem in the image reads:

"Diketahui lingkaran dengan sudut pusat 180° dan keliling lingkarannya 50π cm, maka luas juring lingkaran tersebut adalah ... cm² (gunakan π = 3,14 dan pembulatan sampai dua angka desimal)."

Translation:
"Given a circle with a central angle of 180° and a circumference of 50π cm, find the area of the sector of the circle. (Use π = 3.14 and round to two decimal places.)"

### Steps to solve:

1. **Find the radius (r):**
   The circumference \( C \) of a circle is given by:
   \[
   C = 2\pi r
   \]
   The problem provides \( C = 50\pi \) cm, so:
   \[
   50\pi = 2\pi r
   \]
   Dividing both sides by \( 2\pi \):
   \[
   r = \frac{50\pi}{2\pi} = 25 \text{ cm}
   \]

2. **Find the area of the full circle:**
   The area \( A \) of a circle is given by:
   \[
   A = \pi r^2
   \]
   Substituting \( r = 25 \) cm and \( \pi = 3.14 \):
   \[
   A = 3.14 \times 25^2 = 3.14 \times 625 = 1962.5 \text{ cm}^2
   \]

3. **Find the area of the sector:**
   The central angle is 180°, which is half of a full circle (360°). Therefore, the area of the sector is half the area of the full circle:
   \[
   \text{Area of sector} = \frac{1}{2} \times 1962.5 = 981.25 \text{ cm}^2
   \]

Thus, the area of the sector is **981.25 cm²**.

---

Would you like further details on the solution or have any other questions?

Here are 5 related questions:
1. How do you calculate the area of a sector when the central angle is not 180°?
2. What is the formula for finding the arc length of a sector?
3. How does the formula for the circumference of a circle relate to the area?
4. If the central angle was 90°, how would the area of the sector change?
5. Can you calculate the radius if only the area of the sector is given?

**Tip:** Always make sure to match the units when calculating area or length to avoid errors.

Diketahui lingkaran dengan sudut pusat 180° dan keliling lingkarannya 50π cm, maka luas juring lingkaran tersebut adalah ... cm² (gunakan π = 3,14 dan pembulatan sampai dua angka desimal).

Learn how to calculate the area of a sector with a 180° central angle and a circumference of 50π cm. This problem includes detailed steps using the formula for the circumference and area of a circle, along with how to find the radius. Suitable for students in Grades 8-10.

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