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: $A = \frac{1}{4} \times \pi \times 3.3^2 = \frac{1}{4} \times 34.21 = 8.55 \text{ cm}^2$

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).