The length of two parallel sides of a trapezium are 30 cm and 50 cm and its height is 16 cm. Its area is :

Options

A. `460 cm^(2) `
B. `750 cm^(2) `
C. `320 cm^(2) `
D. `640 cm^(2) `

Answer

To find the area of the trapezium, we can follow these steps:

### Step 1: Identify the lengths of the parallel sides and the height
The lengths of the two parallel sides of the trapezium are given as:
- Side 1 (a) = 30 cm
- Side 2 (b) = 50 cm
- Height (h) = 16 cm

### Step 2: Use the formula for the area of a trapezium
The formula for the area (A) of a trapezium is:
\[ A = \frac{1}{2} \times (a + b) \times h \]

### Step 3: Substitute the values into the formula
Now, substitute the values of the parallel sides and the height into the formula:
\[ A = \frac{1}{2} \times (30 + 50) \times 16 \]

### Step 4: Calculate the sum of the parallel sides
First, calculate the sum of the parallel sides:
\[ 30 + 50 = 80 \]

### Step 5: Calculate the area
Now substitute this sum back into the area formula:
\[ A = \frac{1}{2} \times 80 \times 16 \]

### Step 6: Simplify the calculation
Calculate \( \frac{1}{2} \times 80 \):
\[ \frac{1}{2} \times 80 = 40 \]

Now multiply this by the height:
\[ A = 40 \times 16 = 640 \]

### Step 7: Final Result
Thus, the area of the trapezium is:
\[ A = 640 \, \text{cm}^2 \]