https://file.aiquickdraw.com/mathbot/file/1728478952669q4v0sov2.jpg

Let's calculate the **omkrets (perimeter)** and **area** for both shapes shown in the image.

### a) Half-circle (radius = 6 cm)

1. **Perimeter (Omkrets)**:
   The perimeter of a half-circle is calculated as the sum of the curved part of the circle and the diameter. 
   - The curved part is half of the circumference of a full circle, which is \( \pi \times d \), where \( d = 2 \times r \).
   - Therefore, the perimeter (O) for a half-circle is: 
   \[
   O = \frac{1}{2} \times 2\pi r + 2r = \pi r + 2r
   \]
   Plugging in \( r = 6 \) cm:
   \[
   O = \pi \times 6 + 2 \times 6 = 18.84 + 12 = 30.84 \text{ cm}
   \]

2. **Area (A)**:
   The area of a half-circle is half of the area of a full circle, which is \( \pi r^2 \). Therefore:
   \[
   A = \frac{1}{2} \times \pi r^2
   \]
   Plugging in \( r = 6 \) cm:
   \[
   A = \frac{1}{2} \times \pi \times 6^2 = \frac{1}{2} \times 113.1 = 56.55 \text{ cm}^2
   \]

### b) Quarter-circle (radius = 3.3 cm)

1. **Perimeter (Omkrets)**:
   The perimeter of a quarter-circle is the sum of the curved part (one-fourth of the circumference of a full circle) and the two straight sides (the radius).
   \[
   O = \frac{1}{4} \times 2\pi r + 2r = \frac{\pi r}{2} + 2r
   \]
   Plugging in \( r = 3.3 \) cm:
   \[
   O = \frac{\pi \times 3.3}{2} + 2 \times 3.3 = 5.18 + 6.6 = 11.78 \text{ cm}
   \]

2. **Area (A)**:
   The area of a quarter-circle is one-fourth of the area of a full circle:
   \[
   A = \frac{1}{4} \times \pi r^2
   \]
   Plugging in \( r = 3.3 \) cm:
   \[
   A = \frac{1}{4} \times \pi \times 3.3^2 = \frac{1}{4} \times 34.21 = 8.55 \text{ cm}^2
   \]

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Let me know if you'd like further details on any part of the calculation or have any questions!

Here are 5 questions for further practice:
1. What would the perimeter of a full circle with radius 6 cm be?
2. How do you find the area of a full circle?
3. If the radius of the half-circle were doubled, what would the new perimeter be?
4. What is the relation between the radius and the area of a circle?
5. Can you calculate the area of a sector with a 60-degree central angle and radius 5 cm?

**Tip:** Always double-check units to ensure that your final answers are in the correct form, especially for area and perimeter (square units for area, regular units for perimeter).

Beräkna omkrets och area för de två cirkelsegmenten.

Learn how to calculate the perimeter and area of semicircles and quarter-circles. This problem covers key geometric concepts including circle formulas and their application to partial circles. Suitable for Grades 7-9 students.

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