Area & perimeter i - Free Printable

To solve the problem of calculating the area and perimeter for each shape in the worksheet, we will use the following formulas:

Formulas:

1. Perimeter of a Rectangle/Square:
\[
\text{Perimeter} = 2 \times (\text{Length} + \text{Width})
\]
For a square, since all sides are equal:
\[
\text{Perimeter} = 4 \times \text{Side}
\]

2. Area of a Rectangle/Square:
\[
\text{Area} = \text{Length} \times \text{Width}
\]
For a square:
\[
\text{Area} = \text{Side}^2
\]

Now, let's calculate the area and perimeter for each shape step by step.

---

Shape (1):

- Dimensions: Length = 9 cm, Width = 7 cm
- Perimeter:
\[
\text{Perimeter} = 2 \times (9 + 7) = 2 \times 16 = 32 \, \text{cm}
\]
- Area:
\[
\text{Area} = 9 \times 7 = 63 \, \text{cm}^2
\]

Answer:
\[
\text{Perimeter: } 32 \, \text{cm}, \quad \text{Area: } 63 \, \text{cm}^2
\]

---

Shape (2):

- Dimensions: Length = 8 cm, Width = 6 cm
- Perimeter:
\[
\text{Perimeter} = 2 \times (8 + 6) = 2 \times 14 = 28 \, \text{cm}
\]
- Area:
\[
\text{Area} = 8 \times 6 = 48 \, \text{cm}^2
\]

Answer:
\[
\text{Perimeter: } 28 \, \text{cm}, \quad \text{Area: } 48 \, \text{cm}^2
\]

---

Shape (3):

- Dimensions: Length = 8 cm, Width = 4 cm
- Perimeter:
\[
\text{Perimeter} = 2 \times (8 + 4) = 2 \times 12 = 24 \, \text{cm}
\]
- Area:
\[
\text{Area} = 8 \times 4 = 32 \, \text{cm}^2
\]

Answer:
\[
\text{Perimeter: } 24 \, \text{cm}, \quad \text{Area: } 32 \, \text{cm}^2
\]

---

Shape (4):

- Dimensions: Side = 5 mm
- Perimeter:
\[
\text{Perimeter} = 4 \times 5 = 20 \, \text{mm}
\]
- Area:
\[
\text{Area} = 5 \times 5 = 25 \, \text{mm}^2
\]

Answer:
\[
\text{Perimeter: } 20 \, \text{mm}, \quad \text{Area: } 25 \, \text{mm}^2
\]

---

Shape (5):

- Dimensions: Length = 5 m, Width = 4 m
- Perimeter:
\[
\text{Perimeter} = 2 \times (5 + 4) = 2 \times 9 = 18 \, \text{m}
\]
- Area:
\[
\text{Area} = 5 \times 4 = 20 \, \text{m}^2
\]

Answer:
\[
\text{Perimeter: } 18 \, \text{m}, \quad \text{Area: } 20 \, \text{m}^2
\]

---

Shape (6):

- Dimensions: Length = 8 mm, Width = 5 mm
- Perimeter:
\[
\text{Perimeter} = 2 \times (8 + 5) = 2 \times 13 = 26 \, \text{mm}
\]
- Area:
\[
\text{Area} = 8 \times 5 = 40 \, \text{mm}^2
\]

Answer:
\[
\text{Perimeter: } 26 \, \text{mm}, \quad \text{Area: } 40 \, \text{mm}^2
\]

---

Shape (7):

- Dimensions: Length = 9 m, Width = 8 m
- Perimeter:
\[
\text{Perimeter} = 2 \times (9 + 8) = 2 \times 17 = 34 \, \text{m}
\]
- Area:
\[
\text{Area} = 9 \times 8 = 72 \, \text{m}^2
\]

Answer:
\[
\text{Perimeter: } 34 \, \text{m}, \quad \text{Area: } 72 \, \text{m}^2
\]

---

Shape (8):

- Dimensions: Length = 9 m, Width = 5 m
- Perimeter:
\[
\text{Perimeter} = 2 \times (9 + 5) = 2 \times 14 = 28 \, \text{m}
\]
- Area:
\[
\text{Area} = 9 \times 5 = 45 \, \text{m}^2
\]

Answer:
\[
\text{Perimeter: } 28 \, \text{m}, \quad \text{Area: } 45 \, \text{m}^2
\]

---

Shape (9):

- Dimensions: Length = 7 mm, Width = 3 mm
- Perimeter:
\[
\text{Perimeter} = 2 \times (7 + 3) = 2 \times 10 = 20 \, \text{mm}
\]
- Area:
\[
\text{Area} = 7 \times 3 = 21 \, \text{mm}^2
\]

Answer:
\[
\text{Perimeter: } 20 \, \text{mm}, \quad \text{Area: } 21 \, \text{mm}^2
\]

---

Shape (10):

- Dimensions: Length = 4 mm, Width = 2 mm
- Perimeter:
\[
\text{Perimeter} = 2 \times (4 + 2) = 2 \times 6 = 12 \, \text{mm}
\]
- Area:
\[
\text{Area} = 4 \times 2 = 8 \, \text{mm}^2
\]

Answer:
\[
\text{Perimeter: } 12 \, \text{mm}, \quad \text{Area: } 8 \, \text{mm}^2
\]

---

Shape (11):

- Dimensions: Length = 10 m, Width = 9 m
- Perimeter:
\[
\text{Perimeter} = 2 \times (10 + 9) = 2 \times 19 = 38 \, \text{m}
\]
- Area:
\[
\text{Area} = 10 \times 9 = 90 \, \text{m}^2
\]

Answer:
\[
\text{Perimeter: } 38 \, \text{m}, \quad \text{Area: } 90 \, \text{m}^2
\]

---

Shape (12):

- Dimensions: Side = 2 mm
- Perimeter:
\[
\text{Perimeter} = 4 \times 2 = 8 \, \text{mm}
\]
- Area:
\[
\text{Area} = 2 \times 2 = 4 \, \text{mm}^2
\]

Answer:
\[
\text{Perimeter: } 8 \, \text{mm}, \quad \text{Area: } 4 \, \text{mm}^2
\]

---

Final Answers:

\[
\boxed{
\begin{array}{ll}
\text{(1)} & \text{Perimeter: } 32 \, \text{cm}, \, \text{Area: } 63 \, \text{cm}^2 \\
\text{(2)} & \text{Perimeter: } 28 \, \text{cm}, \, \text{Area: } 48 \, \text{cm}^2 \\
\text{(3)} & \text{Perimeter: } 24 \, \text{cm}, \, \text{Area: } 32 \, \text{cm}^2 \\
\text{(4)} & \text{Perimeter: } 20 \, \text{mm}, \, \text{Area: } 25 \, \text{mm}^2 \\
\text{(5)} & \text{Perimeter: } 18 \, \text{m}, \, \text{Area: } 20 \, \text{m}^2 \\
\text{(6)} & \text{Perimeter: } 26 \, \text{mm}, \, \text{Area: } 40 \, \text{mm}^2 \\
\text{(7)} & \text{Perimeter: } 34 \, \text{m}, \, \text{Area: } 72 \, \text{m}^2 \\
\text{(8)} & \text{Perimeter: } 28 \, \text{m}, \, \text{Area: } 45 \, \text{m}^2 \\
\text{(9)} & \text{Perimeter: } 20 \, \text{mm}, \, \text{Area: } 21 \, \text{mm}^2 \\
\text{(10)} & \text{Perimeter: } 12 \, \text{mm}, \, \text{Area: } 8 \, \text{mm}^2 \\
\text{(11)} & \text{Perimeter: } 38 \, \text{m}, \, \text{Area: } 90 \, \text{m}^2 \\
\text{(12)} & \text{Perimeter: } 8 \, \text{mm}, \, \text{Area: } 4 \, \text{mm}^2 \\
\end{array}
}
\]