The lengths of two parallel sides of a trapezium are 12 cm and 16 cm. If the height of the trapezium be 8 cm, then its area is

Options

A. 189 sq. cm
B. 146 sq. cm
C. 112 sq. cm
D. 120 sq. cm

Answer

To find the area of the trapezium with parallel sides of lengths 12 cm and 16 cm and a height of 8 cm, we can follow these steps:

### Step 1: Identify the formula for the area of a trapezium.
The area \( A \) of a trapezium can be calculated using the formula:
\[ A = \frac{1}{2} \times (a + b) \times h \]
where \( a \) and \( b \) are the lengths of the two parallel sides, and \( h \) is the height.

### Step 2: Substitute the known values into the formula.
From the problem, we know:
- Length of the first parallel side \( a = 12 \) cm
- Length of the second parallel side \( b = 16 \) cm
- Height \( h = 8 \) cm

Now, substitute these values into the formula:
\[ A = \frac{1}{2} \times (12 + 16) \times 8 \]

### Step 3: Calculate the sum of the parallel sides.
First, calculate the sum of the parallel sides:
\[ 12 + 16 = 28 \]

### Step 4: Substitute the sum back into the area formula.
Now substitute this sum back into the area formula:
\[ A = \frac{1}{2} \times 28 \times 8 \]

### Step 5: Calculate the area.
Now calculate the area:
\[ A = \frac{1}{2} \times 28 \times 8 = 14 \times 8 = 112 \text{ cm}^2 \]

### Conclusion
Thus, the area of the trapezium is \( 112 \text{ cm}^2 \).

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