Area and Perimeter Answer Key

Problem Analysis:

The task involves calculating the area and perimeter of various shapes based on given dimensions. The shapes include rectangles and squares, and the solution requires applying basic formulas for area and perimeter.

#### Formulas:
1. Area of a Rectangle:
\[
\text{Area} = \text{length} \times \text{width}
\]

2. Perimeter of a Rectangle:
\[
\text{Perimeter} = 2 \times (\text{length} + \text{width})
\]

3. Area of a Square:
\[
\text{Area} = \text{side} \times \text{side}
\]

4. Perimeter of a Square:
\[
\text{Perimeter} = 4 \times \text{side}
\]

Solution to Each Part:

#### Part (a):
- Given: A rectangle with length \( l = 12 \) cm and width \( w = 8 \) cm.
- Task: Calculate the area and perimeter.

1. Area:
\[
\text{Area} = l \times w = 12 \, \text{cm} \times 8 \, \text{cm} = 96 \, \text{cm}^2
\]

2. Perimeter:
\[
\text{Perimeter} = 2 \times (l + w) = 2 \times (12 \, \text{cm} + 8 \, \text{cm}) = 2 \times 20 \, \text{cm} = 40 \, \text{cm}
\]

- Answer:
\[
\boxed{96 \, \text{cm}^2, 40 \, \text{cm}}
\]

#### Part (b):
- Given: A square with side length \( s = 5 \) cm.
- Task: Calculate the area and perimeter.

1. Area:
\[
\text{Area} = s \times s = 5 \, \text{cm} \times 5 \, \text{cm} = 25 \, \text{cm}^2
\]

2. Perimeter:
\[
\text{Perimeter} = 4 \times s = 4 \times 5 \, \text{cm} = 20 \, \text{cm}
\]

- Answer:
\[
\boxed{25 \, \text{cm}^2, 20 \, \text{cm}}
\]

#### Part (c):
- Given: A rectangle with length \( l = 16 \) cm and width \( w = 3 \) cm.
- Task: Calculate the area and perimeter.

1. Area:
\[
\text{Area} = l \times w = 16 \, \text{cm} \times 3 \, \text{cm} = 48 \, \text{cm}^2
\]

2. Perimeter:
\[
\text{Perimeter} = 2 \times (l + w) = 2 \times (16 \, \text{cm} + 3 \, \text{cm}) = 2 \times 19 \, \text{cm} = 38 \, \text{cm}
\]

- Answer:
\[
\boxed{48 \, \text{cm}^2, 38 \, \text{cm}}
\]

Final Answer:

\[
\boxed{96 \, \text{cm}^2, 40 \, \text{cm}; \, 25 \, \text{cm}^2, 20 \, \text{cm}; \, 48 \, \text{cm}^2, 38 \, \text{cm}}
\]