Calculate the perimeters of the following shapes, using pi = 22/7 where needed. Shape 1 is a semicircle with diameter 14 cm. Shape 2 is composed of a quarter circle, a semicircle, and a straight line

here are the perimeters of the shapes:

1)
This shape is a semicircle.

Step 1: Calculate the length of the curved part.
The diameter ($d$) is $14 \text{ cm}$. The curved part is half the circumference of a circle. The formula for the circumference of a circle is $C = \pi d$. We are given $\pi = \frac{22}{7}$.

$$\text{Length of curved part} = \frac{1}{2} \pi d = \frac{1}{2} \times \frac{22}{7} \times 14 \text{ cm}$$ $$\text{Length of curved part} = 11 \times 2 \text{ cm} = 22 \text{ cm}$$

Step 2: Calculate the total perimeter.
The perimeter is the sum of the straight side (diameter) and the curved part.

$$\text{Perimeter} = 14 \text{ cm} + 22 \text{ cm}$$ $$\text{Perimeter} = 36 \text{ cm}$$

The perimeter of shape 1 is $\boxed{\text{36 cm}}$.

2)
This shape consists of a quarter circle, a semicircle, and a straight line segment.

Step 1: Identify the dimensions.
The straight line segment is $7 \text{ cm}$. This is the radius of the quarter circle ($r_1 = 7 \text{ cm}$) and also the diameter of the semicircle ($d_2 = 7 \text{ cm}$).

Step 2: Calculate the arc length of the quarter circle.

$$\text{Arc length of quarter circle} = \frac{1}{4} (2 \pi r_1) = \frac{1}{2} \pi r_1 = \frac{1}{2} \times \frac{22}{7} \times 7 \text{ cm}$$ $$\text{Arc length of quarter circle} = 11 \text{ cm}$$

Step 3: Calculate the arc length of the semicircle.

$$\text{Arc length of semicircle} = \frac{1}{2} (\pi d_2) = \frac{1}{2} \times \frac{22}{7} \times 7 \text{ cm}$$ $$\text{Arc length of semicircle} = 11 \text{ cm}$$

Step 4: Calculate the total perimeter.

$$\text{Perimeter} = (\text{arc length of quarter circle}) + (\text{arc length of semicircle}) + (\text{straight line segment})$$ $$\text{Perimeter} = 11 \text{ cm} + 11 \text{ cm} + 7 \text{ cm}$$ $$\text{Perimeter} = 29 \text{ cm}$$

The perimeter of shape 2 is $\boxed{\text{29 cm}}$.

3)
This shape is a rectangle with a semicircle cut out from the top.

Step 1: Identify the lengths of the straight sides.
The bottom side is $9 \text{ cm}$. The two vertical sides are $5 \text{ cm}$ each. The two small straight segments on the top are $1 \text{ cm}$ each.

Step 2: Determine the diameter of the inner semicircle.
The total length of the top edge of the rectangle is $9 \text{ cm}$. The two small straight segments are $1 \text{ cm}$ each. So, the diameter of the semicircle ($d$) is $9 \text{ cm} - 1 \text{ cm} - 1 \text{ cm} = 7 \text{ cm}$.

Step 3: Calculate the arc length of the inner semicircle.

$$\text{Arc length of semicircle} = \frac{1}{2} \pi d = \frac{1}{2} \times \frac{22}{7} \times 7 \text{ cm}$$ $$\text{Arc length of semicircle} = 11 \text{ cm}$$

Step 4: Calculate the total perimeter.

$$\text{Perimeter} = (\text{bottom side}) + (\text{two vertical sides}) + (\text{two top straight segments}) + (\text{arc length of inner semicircle})$$ $$\text{Perimeter} = 9 \text{ cm} + (2 \times 5 \text{ cm}) + (2 \times 1 \text{ cm}) + 11 \text{ cm}$$ $$\text{Perimeter} = 9 \text{ cm} + 10 \text{ cm} + 2 \text{ cm} + 11 \text{ cm}$$ $$\text{Perimeter} = 32 \text{ cm}$$

The perimeter of shape 3 is $\boxed{\text{32 cm}}$.

4)
This shape is composed of four semicircles.

Step 1: Identify the diameter of each semicircle.
The dashed lines indicate a central square with sides of $7 \text{ cm}$. Each semicircle has a diameter ($d$) equal to the side of this square, so $d = 7 \text{ cm}$.

Step 2: Calculate the arc length of one semicircle.

$$\text{Arc length of one semicircle} = \frac{1}{2} \pi d = \frac{1}{2} \times \frac{22}{7} \times 7 \text{ cm}$$ $$\text{Arc length of one semicircle} = 11 \text{ cm}$$

Step 3: Calculate the total perimeter.
Since there are four such semicircles, the total perimeter is four times the arc length of one semicircle.

$$\text{Perimeter} = 4 \times 11 \text{ cm}$$ $$\text{Perimeter} = 44 \text{ cm}$$

The perimeter of shape 4 is $\boxed{\text{44 cm}}$.

5)
This shape is a rectangle with two semicircles on its ends.

Step 1: Identify the dimensions.
The '7' indicates the length of the straight rectangular part is $7 \text{ cm}$. The vertical dashed lines show that the diameter of each semicircle ($d$) is also $7 \text{ cm}$.

Step 2: Calculate the total perimeter.
The perimeter consists of two straight sides and the circumference of one full circle (formed by the two semicircles).

$$\text{Perimeter} = (2 \times \text{length of straight side}) + (\pi d)$$ $$$$