The length of two parallel sides of a trapezium are 10 cm and 13 cm. If the area of the trapezium is 460 `cm^(2)`, then what is the value (in cm) of its height?

Options

A. 42
B. 40
C. 36
D. 48

Answer

To find the height of the trapezium given the lengths of the parallel sides and the area, we can use the formula for the area of a trapezium:

\[ \text{Area} = \frac{1}{2} \times (A + B) \times H \]

where \(A\) and \(B\) are the lengths of the parallel sides, and \(H\) is the height.

### Step-by-Step Solution:

1. **Identify the lengths of the parallel sides**:
- Let \(A = 10 \, \text{cm}\) (length of one parallel side)
- Let \(B = 13 \, \text{cm}\) (length of the other parallel side)

2. **Write down the area of the trapezium**:
- Given area = \(460 \, \text{cm}^2\)

3. **Substitute the values into the area formula**:
\[ 460 = \frac{1}{2} \times (10 + 13) \times H \]

4. **Simplify the expression**:
- Calculate \(10 + 13\):
\[ 10 + 13 = 23 \]
- Substitute back into the equation:
\[ 460 = \frac{1}{2} \times 23 \times H \]

5. **Multiply both sides by 2 to eliminate the fraction**:
\[ 920 = 23 \times H \]

6. **Solve for \(H\)**:
\[ H = \frac{920}{23} \]

7. **Calculate the value of \(H\)**:
- Perform the division:
\[ H = 40 \, \text{cm} \]

### Final Answer:
The height of the trapezium is \(40 \, \text{cm}\).