https://file.aiquickdraw.com/mathbot/file/1725919844927xdumc1z1.jpg

We are asked to solve the following question based on the provided figure:

In the figure:
- Arcs \( PS \) and \( QR \) are semicircles with a radius of \( 3.5 \, \text{cm} \).
- The straight lines \( PQ \) and \( SR \) have a length of \( 9 \, \text{cm} \).
- The value of \( \pi \) is approximated as \( \frac{22}{7} \).

We need to calculate:
1. **The perimeter** of the figure \( PQRS \).
2. **The area** of the figure \( PQRS \).

### Part (i): Perimeter

The perimeter of the figure consists of:
- Two straight lines: \( PQ \) and \( SR \), both measuring \( 9 \, \text{cm} \).
- Two semicircles: \( PS \) and \( QR \), each with radius \( 3.5 \, \text{cm} \).

The perimeter of a semicircle is given by:
\[
P_{\text{semicircle}} = \frac{1}{2} \times 2\pi r = \pi r
\]
Where \( r = 3.5 \, \text{cm} \), and \( \pi = \frac{22}{7} \).

For each semicircle:
\[
P_{\text{semicircle}} = \frac{22}{7} \times 3.5 = 11 \, \text{cm}
\]

Since there are two semicircles, the total perimeter from the semicircles is:
\[
P_{\text{semicircles}} = 11 + 11 = 22 \, \text{cm}
\]

Now, adding the lengths of the straight lines \( PQ \) and \( SR \):
\[
P_{\text{total}} = 9 + 9 + 22 = 40 \, \text{cm}
\]

Thus, the perimeter is **40 cm**.

### Part (ii): Area

The area of the figure can be found by subtracting the areas of the two semicircles from the area of the rectangle formed by \( PQ \) and \( SR \).

1. **Area of the rectangle**:  
   The area of the rectangle is given by:
   \[
   A_{\text{rectangle}} = \text{length} \times \text{width} = PQ \times 2r = 9 \times (2 \times 3.5) = 9 \times 7 = 63 \, \text{cm}^2
   \]

2. **Area of the semicircles**:  
   The area of a semicircle is:
   \[
   A_{\text{semicircle}} = \frac{1}{2} \pi r^2
   \]
   For each semicircle with \( r = 3.5 \):
   \[
   A_{\text{semicircle}} = \frac{1}{2} \times \frac{22}{7} \times (3.5)^2 = \frac{1}{2} \times \frac{22}{7} \times 12.25 = \frac{1}{2} \times 38.5 = 19.25 \, \text{cm}^2
   \]

Since there are two semicircles:
\[
A_{\text{semicircles}} = 19.25 \times 2 = 38.5 \, \text{cm}^2
\]

3. **Area of the figure**:  
   Subtract the area of the semicircles from the area of the rectangle:
   \[
   A_{\text{figure}} = A_{\text{rectangle}} - A_{\text{semicircles}} = 63 - 38.5 = 24.5 \, \text{cm}^2
   \]

Thus, the area is **24.5 cm²**.

### Summary:
1. The perimeter of the figure is **40 cm**.
2. The area of the figure is **24.5 cm²**.

Would you like further details or have any other questions?

Here are 5 relative questions for deeper understanding:
1. How do we calculate the circumference of a full circle?
2. Why do we use half the area formula for semicircles?
3. How can we convert the units from cm to meters?
4. Can the formula for a semicircle's perimeter change for different units of π?
5. How would the perimeter change if the radius was doubled?

**Tip:** Always ensure you correctly identify which parts of a figure are straight lines versus curved lines when calculating perimeter.

Calculate the perimeter and area of a figure involving semicircles and straight lines. The semicircles have a radius of 3.5 cm, and the lengths of the straight sides are 9 cm. Use π = 22/7.

Learn how to calculate the perimeter and area of a figure consisting of two semicircles and two straight lines. The problem involves using the formula for the perimeter and area of semicircles, as well as the area of rectangles. Suitable for students in Grades 7-9.

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