The perimeter of a trapezium is 52 cm and its non-parallel sides are 9 cm and 11 cm respectively. If its height is 8 cm. find the area of traplezium.

Answer

To find the area of the trapezium given the perimeter, non-parallel sides, and height, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Information:**
- Perimeter of the trapezium = 52 cm
- Non-parallel sides = 9 cm and 11 cm
- Height = 8 cm

2. **Set Up the Equation for the Perimeter:**
The perimeter of a trapezium is given by the formula:
\[ \text{Perimeter} = \text{Side}_1 + \text{Side}_2 + \text{Base}_1 + \text{Base}_2 \]
Here, let the lengths of the parallel sides (bases) be \( A \) and \( B \). Therefore, we can write:
\[ 9 + 11 + A + B = 52 \]

3. **Simplify the Equation:**
Combine the known side lengths:
\[ 20 + A + B = 52 \]
Subtract 20 from both sides:
\[ A + B = 52 - 20 \]
\[ A + B = 32 \quad \text{(Equation 1)} \]

4. **Use the Area Formula for a Trapezium:**
The area \( A \) of a trapezium is given by:
\[ \text{Area} = \frac{1}{2} \times \text{Height} \times (\text{Base}_1 + \text{Base}_2) \]
Substituting the known values:
\[ \text{Area} = \frac{1}{2} \times 8 \times (A + B) \]

5. **Substitute the Value of \( A + B \):**
From Equation 1, we know \( A + B = 32 \):
\[ \text{Area} = \frac{1}{2} \times 8 \times 32 \]

6. **Calculate the Area:**
First, simplify \( \frac{1}{2} \times 8 \):
\[ 4 \times 32 = 128 \]
Therefore, the area of the trapezium is:
\[ \text{Area} = 128 \, \text{cm}^2 \]

### Final Answer:
The area of the trapezium is **128 cm²**.