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.