Independent practice worksheet for calculating area and perimeter of triangles, parallelograms, and trapezoids.

Problem: Solve the given problems related to the area and perimeter of triangles, parallelograms, and trapezoids.

#### 1. Find the area and perimeter of the parallelogram.

Given:
- Base = 6 cm
- Height = 5 cm
- Side lengths = 5 cm (two sides) and 6 cm (two sides)

Solution:

##### Area of the parallelogram:
The formula for the area of a parallelogram is:
\[
\text{Area} = \text{base} \times \text{height}
\]
Substitute the given values:
\[
\text{Area} = 6 \, \text{cm} \times 5 \, \text{cm} = 30 \, \text{cm}^2
\]

##### Perimeter of the parallelogram:
The formula for the perimeter of a parallelogram is:
\[
\text{Perimeter} = 2 \times (\text{base} + \text{side})
\]
Here, the base is 6 cm, and the side is 5 cm:
\[
\text{Perimeter} = 2 \times (6 \, \text{cm} + 5 \, \text{cm}) = 2 \times 11 \, \text{cm} = 22 \, \text{cm}
\]

Final Answer for Parallelogram:
\[
\boxed{\text{Area} = 30 \, \text{cm}^2, \, \text{Perimeter} = 22 \, \text{cm}}
\]

---

#### 2. Find the area and perimeter of the trapezium.

Given:
- Parallel sides: 8 cm and 12 cm
- Height: 5 cm
- Non-parallel sides: 5 cm and 7 cm

Solution:

##### Area of the trapezium:
The formula for the area of a trapezium is:
\[
\text{Area} = \frac{1}{2} \times (\text{sum of parallel sides}) \times \text{height}
\]
Substitute the given values:
\[
\text{Area} = \frac{1}{2} \times (8 \, \text{cm} + 12 \, \text{cm}) \times 5 \, \text{cm} = \frac{1}{2} \times 20 \, \text{cm} \times 5 \, \text{cm} = 50 \, \text{cm}^2
\]

##### Perimeter of the trapezium:
The perimeter is the sum of all the sides:
\[
\text{Perimeter} = 8 \, \text{cm} + 12 \, \text{cm} + 5 \, \text{cm} + 7 \, \text{cm} = 32 \, \text{cm}
\]

Final Answer for Trapezium:
\[
\boxed{\text{Area} = 50 \, \text{cm}^2, \, \text{Perimeter} = 32 \, \text{cm}}
\]

---

#### 3. Find the area and perimeter of the triangle.

Given:
- Base = 7 cm
- Height = 4 cm
- Sides: 5 cm, 7 cm, and 8 cm

Solution:

##### Area of the triangle:
The formula for the area of a triangle is:
\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
\]
Substitute the given values:
\[
\text{Area} = \frac{1}{2} \times 7 \, \text{cm} \times 4 \, \text{cm} = \frac{1}{2} \times 28 \, \text{cm}^2 = 14 \, \text{cm}^2
\]

##### Perimeter of the triangle:
The perimeter is the sum of all the sides:
\[
\text{Perimeter} = 5 \, \text{cm} + 7 \, \text{cm} + 8 \, \text{cm} = 20 \, \text{cm}
\]

Final Answer for Triangle:
\[
\boxed{\text{Area} = 14 \, \text{cm}^2, \, \text{Perimeter} = 20 \, \text{cm}}
\]

---

#### 4. Find the area and perimeter of the parallelogram.

Given:
- Base = 8 cm
- Height = 6 cm
- Side lengths: 8 cm (one side) and 10 cm (adjacent side)

Solution:

##### Area of the parallelogram:
The formula for the area of a parallelogram is:
\[
\text{Area} = \text{base} \times \text{height}
\]
Substitute the given values:
\[
\text{Area} = 8 \, \text{cm} \times 6 \, \text{cm} = 48 \, \text{cm}^2
\]

##### Perimeter of the parallelogram:
The formula for the perimeter of a parallelogram is:
\[
\text{Perimeter} = 2 \times (\text{base} + \text{side})
\]
Here, the base is 8 cm, and the side is 10 cm:
\[
\text{Perimeter} = 2 \times (8 \, \text{cm} + 10 \, \text{cm}) = 2 \times 18 \, \text{cm} = 36 \, \text{cm}
\]

Final Answer for Parallelogram:
\[
\boxed{\text{Area} = 48 \, \text{cm}^2, \, \text{Perimeter} = 36 \, \text{cm}}
\]

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Summary of Final Answers:

1. Parallelogram: \(\boxed{\text{Area} = 30 \, \text{cm}^2, \, \text{Perimeter} = 22 \, \text{cm}}\)
2. Trapezium: \(\boxed{\text{Area} = 50 \, \text{cm}^2, \, \text{Perimeter} = 32 \, \text{cm}}\)
3. Triangle: \(\boxed{\text{Area} = 14 \, \text{cm}^2, \, \text{Perimeter} = 20 \, \text{cm}}\)
4. Parallelogram: \(\boxed{\text{Area} = 48 \, \text{cm}^2, \, \text{Perimeter} = 36 \, \text{cm}}\)