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.