The area of a trapezium whose parallel sides are 9 cm & 16 cm and the distance between these sides is 8 cm, is

Options

A. 60 `cm^(2)`
B. 72 `cm^(2)`
C. 56 `cm^(2)`
D. 100 `cm^(2)`

Answer

To find the area of the trapezium with parallel sides measuring 9 cm and 16 cm, and the distance between these sides being 8 cm, we can use the formula for the area of a trapezium:

### Step-by-Step Solution:

1. **Identify the lengths of the parallel sides and the height**:
- Let the lengths of the parallel sides be \( a = 9 \) cm and \( b = 16 \) cm.
- The height (distance between the parallel sides) is \( h = 8 \) cm.

2. **Use the area formula for a trapezium**:
- The formula for the area \( A \) of a trapezium is given by:
\[ A = \frac{1}{2} \times (a + b) \times h \]

3. **Substitute the values into the formula**:
- Substitute \( a = 9 \) cm, \( b = 16 \) cm, and \( h = 8 \) cm into the formula:
\[ A = \frac{1}{2} \times (9 + 16) \times 8 \]

4. **Calculate the sum of the parallel sides**:
- Calculate \( 9 + 16 \):
\[ 9 + 16 = 25 \]

5. **Calculate the area**:
- Now substitute back into the area formula:
\[ A = \frac{1}{2} \times 25 \times 8 \]
- Calculate \( \frac{1}{2} \times 25 = 12.5 \):
\[ A = 12.5 \times 8 \]
- Now calculate \( 12.5 \times 8 \):
\[ A = 100 \text{ cm}^2 \]

6. **Final Result**:
- The area of the trapezium is \( 100 \text{ cm}^2 \).