Calculate the perimeter of the L-shaped figure A and the T-shaped figure B.

4.1

Step 1: Identify all side lengths of the L-shaped figure.
The given sides are $4 \text{ cm}$, $1 \text{ cm}$, $1 \text{ cm}$, and $3 \text{ cm}$.
There are two missing sides.
The total vertical length on the left is $4 \text{ cm}$. The visible vertical segment on the right is $1 \text{ cm}$. Therefore, the hidden vertical segment is $4 \text{ cm} - 1 \text{ cm} = 3 \text{ cm}$.
The total horizontal length at the bottom is $3 \text{ cm}$. The visible horizontal segment at the top is $1 \text{ cm}$. Therefore, the hidden horizontal segment is $3 \text{ cm} - 1 \text{ cm} = 2 \text{ cm}$.

Step 2: Calculate the perimeter by summing all outer side lengths.

$$P = 4 \text{ cm} + 1 \text{ cm} + 2 \text{ cm} + 1 \text{ cm} + 3 \text{ cm} + 3 \text{ cm}$$ $$P = 14 \text{ cm}$$

The perimeter of figure A is $\boxed{\text{14 cm}}$.

4.2

Step 1: Identify all side lengths of the T-shaped figure.
The given sides are $5 \text{ cm}$, $0.5 \text{ cm}$, $3.5 \text{ cm}$, and $3 \text{ cm}$.
Due to symmetry, the other small vertical side is $0.5 \text{ cm}$, and the other main vertical side is $3.5 \text{ cm}$.
The top horizontal length is $5 \text{ cm}$ and the bottom horizontal length is $3 \text{ cm}$. The two small horizontal segments connecting the top and bottom parts are equal.
Length of each small horizontal segment = $\frac{5 \text{ cm} - 3 \text{ cm}}{2} = \frac{2 \text{ cm}}{2} = 1 \text{ cm}$.

Step 2: Calculate the perimeter by summing all outer side lengths.

$$P = 5 \text{ cm} + 0.5 \text{ cm} + 1 \text{ cm} + 3.5 \text{ cm} + 3 \text{ cm} + 3.5 \text{ cm} + 1 \text{ cm} + 0.5 \text{ cm}$$ $$P = 18 \text{ cm}$$

The perimeter of figure B is $\boxed{\text{18 cm}}$.

4.3

Step 1: Convert all units to centimeters.
The top side is $90 \text{ cm}$.
The right slant side is $86.02 \text{ cm}$.
The bottom base consists of three segments: $500 \text{ mm}$, $90 \text{ cm}$, and $500 \text{ mm}$.
Convert $500 \text{ mm}$ to centimeters: $500 \text{ mm} = 50 \text{ cm}$.
The total bottom base length is $50 \text{ cm} + 90 \text{ cm} + 50 \text{ cm} = 190 \text{ cm}$.

Step 2: Calculate the length of the left slant side.
The figure shows a right-angled triangle on the left with a base of $50 \text{ cm}$ and a height of $70 \text{ cm}$. Use the Pythagorean theorem: $a^2 + b^2 = c^2$.

$$c = \sqrt{(50 \text{ cm})^2 + (70 \text{ cm})^2}$$ $$c = \sqrt{2500 \text{ cm}^2 + 4900 \text{ cm}^2}$$ $$c = \sqrt{7400 \text{ cm}^2}$$ $$c \approx 86.023 \text{ cm}$$

Rounding to two decimal places, the left slant side is approximately $86.02 \text{ cm}$.

Step 3: Calculate the perimeter by summing all four side lengths.

$$P = \text{top side} + \text{bottom side} + \text{left slant side} + \text{right slant side}$$ $$P = 90 \text{ cm} + 190 \text{ cm} + 86.02 \text{ cm} + 86.02 \text{ cm}$$ $$P = 452.04 \text{ cm}$$

The perimeter of the trapezium is $\boxed{\text{452.04 cm}}$.

4.4

Step 1: Identify the components of the figure and state assumptions.
The figure consists of a rectangular base and a semicircle on top.
The vertical side of the rectangular part is given as $47 \text{ mm}$.
Assumption: Since no other horizontal dimension is given, we assume the rectangular part is a square, meaning its width is also $47 \text{ mm}$. This width is also the diameter of the semicircle.

Step 2: Calculate the perimeter.
The perimeter consists of:

• Two vertical sides of the rectangle: $47 \text{ mm} + 47 \text{ mm}$
• The bottom horizontal side of the rectangle: $47 \text{ mm}$ (based on assumption)
• The arc length of the semicircle: $\frac{1}{2} \times \pi \times \text{diameter}$

$$P = 47 \text{ mm} + 47 \text{ mm} + 47 \text{ mm} + \frac{1}{2} \pi (47 \text{ mm})$$ $$P = 141 \text{ mm} + \frac{47}{2} \pi \text{ mm}$$ $$P \approx 141 \text{ mm} + 23.5 \times 3.14159 \text{ mm}$$ $$$$