The two parallel sides of trapezium are 1 metre and 2 metre respectively .The perpendicular distance between them is 6 metres .The area of the trapezium is -----

Options

A. 18 sq. metres
B. 12 sq metres
C. 9 sq. metres
D. 6 sq. metres

Answer

To find the area of the trapezium, we can use the formula:

\[ \text{Area} = \frac{1}{2} \times (l_1 + l_2) \times h \]

where:
- \( l_1 \) and \( l_2 \) are the lengths of the two parallel sides,
- \( h \) is the height (the perpendicular distance between the parallel sides).

### Step 1: Identify the values
From the question, we have:
- \( l_1 = 1 \) metre (the length of the first parallel side)
- \( l_2 = 2 \) metres (the length of the second parallel side)
- \( h = 6 \) metres (the perpendicular distance between the parallel sides)

### Step 2: Substitute the values into the formula
Now, we substitute these values into the area formula:

\[ \text{Area} = \frac{1}{2} \times (1 + 2) \times 6 \]

### Step 3: Simplify the expression
First, calculate \( l_1 + l_2 \):

\[ l_1 + l_2 = 1 + 2 = 3 \]

Now substitute this back into the area formula:

\[ \text{Area} = \frac{1}{2} \times 3 \times 6 \]

### Step 4: Calculate the area
Now, calculate \( \frac{1}{2} \times 3 \):

\[ \frac{1}{2} \times 3 = 1.5 \]

Next, multiply by the height:

\[ \text{Area} = 1.5 \times 6 = 9 \]

### Final Answer
Thus, the area of the trapezium is:

\[ \text{Area} = 9 \text{ square metres} \]

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