https://file.aiquickdraw.com/mathbot/file/17279833982962gnr2g5a.jpg

Let's go through the calculations for each of the diagrams shown in the image, aiming to find the shaded (diarsir) area.

### (i) **Square with a circle inside:**
- The side of the square is given as 10 cm.
- The circle is inscribed in the square, meaning the diameter of the circle is also 10 cm.
- The area of the square:
  \[
  A_{\text{square}} = \text{side}^2 = 10^2 = 100 \, \text{cm}^2
  \]
- The radius of the circle is half of the diameter:
  \[
  r = \frac{10}{2} = 5 \, \text{cm}
  \]
  The area of the circle:
  \[
  A_{\text{circle}} = \pi r^2 = \pi (5)^2 = 25\pi \approx 78.54 \, \text{cm}^2
  \]
- The shaded area is the difference between the area of the square and the area of the circle:
  \[
  A_{\text{shaded}} = A_{\text{square}} - A_{\text{circle}} = 100 - 78.54 \approx 21.46 \, \text{cm}^2
  \]

### (ii) **Quarter-circle:**
- The radius of the quarter-circle is 21 cm.
- The area of a full circle with radius 21 cm:
  \[
  A_{\text{circle}} = \pi r^2 = \pi (21)^2 = 441\pi \approx 1385.44 \, \text{cm}^2
  \]
- Since this is a quarter of a circle, the area of the quarter-circle is:
  \[
  A_{\text{quarter-circle}} = \frac{1}{4} \times 1385.44 \approx 346.36 \, \text{cm}^2
  \]
- There is no direct shading described for this problem, so this may be part of a composite figure, but assuming it's just the quarter circle area, it's approximately:
  \[
  346.36 \, \text{cm}^2
  \]

### (iii) **Rectangle with two half-circles removed:**
- The dimensions of the rectangle are given as 13 cm (length) and 7 cm (height).
- The radius of each half-circle is half of the height of the rectangle, which is:
  \[
  r = \frac{7}{2} = 3.5 \, \text{cm}
  \]
- The area of the rectangle:
  \[
  A_{\text{rectangle}} = \text{length} \times \text{height} = 13 \times 7 = 91 \, \text{cm}^2
  \]
- The area of a full circle with radius 3.5 cm:
  \[
  A_{\text{circle}} = \pi (3.5)^2 = \pi (12.25) = 38.48 \, \text{cm}^2
  \]
- The area of the two half-circles is equal to one full circle, so the area removed by the two half-circles is:
  \[
  A_{\text{removed}} = 38.48 \, \text{cm}^2
  \]
- The shaded area is the difference between the area of the rectangle and the area of the removed circles:
  \[
  A_{\text{shaded}} = 91 - 38.48 \approx 52.52 \, \text{cm}^2
  \]

### Final results:
1. Shaded area for (i): **21.46 cm²**
2. Shaded area for (ii): **346.36 cm²**
3. Shaded area for (iii): **52.52 cm²**

Would you like more details on any of these calculations or further clarification?

### Related questions:
1. How do you calculate the area of a semicircle?
2. What is the difference between the circumference and the area of a circle?
3. How would the area change if the radius of the circle in (i) was doubled?
4. How do you find the area of a sector of a circle?
5. What is the formula for the area of a composite shape like in (iii)?

### Tip:
Always use consistent units when working with area or volume calculations to avoid confusion or errors in your final result.

Hitung luas daerah yang diarsir untuk bentuk (i), (ii), dan (iii).

Learn how to calculate the shaded area for composite geometric shapes, including a square with an inscribed circle, a quarter-circle, and a rectangle with two semicircles removed. This problem explores key geometric concepts, suitable for students in Grades 8-10.

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