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To solve this problem, we need to find the area of the shaded region \( WXYZ \). The shaded area is the difference between the areas of the two sectors, one with a radius of 34 cm (sector \( OWX \)) and the other with a radius of 23 cm (sector \( OYZ \)).

### Step 1: Formula for the Area of a Sector
The formula for the area \( A \) of a sector with radius \( r \) and angle \( \theta \) (in degrees) is given by:
\[
A = \frac{\theta}{360} \times \pi r^2
\]
where:
- \( r \) is the radius of the sector,
- \( \theta \) is the central angle in degrees,
- \( \pi \) is approximately 3.14159.

### Step 2: Area of Sector \( OWX \) (radius = 34 cm, angle = 75°)
\[
A_{\text{OWX}} = \frac{75}{360} \times \pi \times (34)^2
\]
\[
A_{\text{OWX}} = \frac{75}{360} \times \pi \times 1156
\]
\[
A_{\text{OWX}} \approx 0.2083 \times 3.14159 \times 1156
\]
\[
A_{\text{OWX}} \approx 757.92 \, \text{cm}^2
\]

### Step 3: Area of Sector \( OYZ \) (radius = 23 cm, angle = 75°)
\[
A_{\text{OYZ}} = \frac{75}{360} \times \pi \times (23)^2
\]
\[
A_{\text{OYZ}} = \frac{75}{360} \times \pi \times 529
\]
\[
A_{\text{OYZ}} \approx 0.2083 \times 3.14159 \times 529
\]
\[
A_{\text{OYZ}} \approx 346.36 \, \text{cm}^2
\]

### Step 4: Shaded Area \( WXYZ \)
The shaded area is the difference between the two sector areas:
\[
A_{\text{shaded}} = A_{\text{OWX}} - A_{\text{OYZ}}
\]
\[
A_{\text{shaded}} = 757.92 - 346.36
\]
\[
A_{\text{shaded}} \approx 411.56 \, \text{cm}^2
\]

Thus, the area of the shaded shape \( WXYZ \) is approximately **411.6 cm²** (rounded to 1 decimal place).

Would you like further details or have any questions?

### Relative Questions:
1. How do we calculate the circumference of a sector?
2. What is the relationship between a sector's area and its central angle?
3. How would the solution change if the central angle was 90° instead of 75°?
4. Can the formula for a sector's area be extended to radians? How?
5. What if one sector was only partially shaded—how would you approach that calculation?

### Tip:
For any geometric problem involving sectors, always ensure that the angle is in degrees or radians and is used correctly in formulas for area or arc length.

OWX is a sector of a circle with a radius of 34 cm. OYZ is a sector of a circle with a radius of 23 cm. The central angle of both sectors is 75°. Work out the area of the shaded shape WXYZ. Give your answer in cm² to 1 d.p.

Learn how to calculate the area of a shaded region formed by two sectors of circles with different radii. The problem involves sectors with radii of 34 cm and 23 cm, and a central angle of 75°. Step-by-step solution included, suitable for students in Grades 8-10.

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