ABCD is a trapezium length of whose parallel sides AB and CD are respectively 10 cm and 12 cm. If midpoint of AD and BC are respectively E and F then length of EF is.

Options

A. 11 cm
B. more than 11 cm
C. less than 11 cm
D. nothing can be said

Answer

To find the length of EF in trapezium ABCD, where AB and CD are the parallel sides, we can follow these steps:

### Step 1: Identify the lengths of the parallel sides
Given:
- Length of AB = 10 cm
- Length of CD = 12 cm

### Step 2: Use the formula for the length of the line segment joining the midpoints of the non-parallel sides
The length of EF, which connects the midpoints E and F of the non-parallel sides AD and BC respectively, can be calculated using the formula:
\[ EF = \frac{1}{2} (AB + CD) \]

### Step 3: Substitute the values into the formula
Now, substitute the lengths of AB and CD into the formula:
\[ EF = \frac{1}{2} (10 \, \text{cm} + 12 \, \text{cm}) \]

### Step 4: Calculate the sum of the lengths
Calculate the sum:
\[ 10 \, \text{cm} + 12 \, \text{cm} = 22 \, \text{cm} \]

### Step 5: Divide by 2 to find EF
Now, divide the sum by 2:
\[ EF = \frac{1}{2} \times 22 \, \text{cm} = 11 \, \text{cm} \]

### Final Answer
Thus, the length of EF is:
\[ \boxed{11 \, \text{cm}} \]

---