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Let's break down the problem step by step to find the perimeter and area of the figure.

### Given:
- A rectangle with dimensions:
  - Length = 9 m
  - Width = 3 m
- Four quadrants, each with a radius of 2 m, are removed from the corners of the rectangle.

### (i) Finding the Perimeter of the Figure
1. **Original Rectangle Perimeter**:  
   The perimeter of the original rectangle = \( 2 \times (\text{length} + \text{width}) = 2 \times (9 + 3) = 2 \times 12 = 24 \) m.

2. **Adjustments Due to Quadrants**:  
   Removing each quadrant means we are removing a quarter-circle from each corner:
   - Total length of the rectangle's edges removed = 4 (number of quadrants) × 2 m (radius of each quadrant) = 8 m.
   - Total arc length added (since the quadrants' edges are part of the perimeter now):
     - The circumference of a full circle = \( 2\pi \times r \).
     - The length of one quadrant = \( \frac{1}{4} \times 2\pi \times 2 = \frac{1}{2}\pi \times 2 = \pi \) m.
     - Total arc length of four quadrants = \( 4 \times \pi = 4\pi \) m.
  
3. **Final Perimeter**:  
   - Original perimeter without the corners = 24 m.
   - Subtract the length removed (8 m) and add the arc length (4π m):
   \[
   \text{Perimeter} = 24 - 8 + 4\pi = 16 + 4\pi \quad \text{meters}.
   \]

### (ii) Finding the Area of the Figure
1. **Original Rectangle Area**:  
   - Area = \( \text{length} \times \text{width} = 9 \times 3 = 27 \) square meters.

2. **Area of Quadrants Removed**:  
   Each quadrant is a quarter of a circle with a radius of 2 m:
   - Area of one circle = \( \pi \times r^2 = \pi \times 2^2 = 4\pi \) square meters.
   - Area of one quadrant = \( \frac{1}{4} \times 4\pi = \pi \) square meters.
   - Total area of four quadrants = \( 4 \times \pi = 4\pi \) square meters.
  
3. **Final Area**:  
   - Area of the figure = Original area - Area of quadrants removed:
   \[
   \text{Area} = 27 - 4\pi \quad \text{square meters}.
   \]

### Final Answers:
1. **Perimeter of the figure**: \( 16 + 4\pi \) meters.
2. **Area of the figure**: \( 27 - 4\pi \) square meters.

Would you like further details or have any questions?

### Related Questions:
1. How would the problem change if the radius of each quadrant were different?
2. What if the quadrants were semicircles instead of quarter circles?
3. How would you calculate the perimeter if only two quadrants were removed?
4. What would be the area of the figure if no quadrants were removed?
5. How would the calculations change if the figure was a square instead of a rectangle?

### Tip:
Always check if a problem involves modifying basic shapes (like adding or removing parts) to make sure you're calculating areas and perimeters correctly!

In the figure, 4 quadrants, each of radius 2 m, are removed from a rectangle. Find (i) the perimeter of the figure, (ii) the area of the figure.

Learn how to calculate the perimeter and area of a rectangle with four quadrants, each of radius 2 meters, removed from its corners. This problem covers key geometric concepts, including perimeter and area of both rectangles and quarter circles. Suitable for students in Grades 7-9.

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