The perimeter of a trapezium is 104 cm, the lengths of its non-parallel sides are 18 cm and 22 cm and its altitude is 16 cm. The area (in `cm^(2)`) of the trapezium is

Options

A. 1024
B. 640
C. 512
D. 320

Answer

To find the area of the trapezium given the perimeter, lengths of the non-parallel sides, and the altitude, we can follow these steps:

### Step 1: Understand the given information
- Perimeter of trapezium (P) = 104 cm
- Length of non-parallel sides = 18 cm and 22 cm
- Altitude (height) = 16 cm

### Step 2: Set up the equation for the perimeter
The perimeter of a trapezium is the sum of the lengths of all its sides. If we denote the lengths of the parallel sides as \( a \) and \( b \), we can write the equation for the perimeter as:
\[ P = a + b + 18 + 22 \]
Substituting the given perimeter:
\[ 104 = a + b + 40 \]

### Step 3: Solve for the sum of the parallel sides
Rearranging the equation to find \( a + b \):
\[ a + b = 104 - 40 = 64 \text{ cm} \]

### Step 4: Use the area formula for the trapezium
The area \( A \) of a trapezium can be calculated using the formula:
\[ A = \frac{1}{2} \times (a + b) \times \text{height} \]
Substituting the values we have:
\[ A = \frac{1}{2} \times 64 \times 16 \]

### Step 5: Calculate the area
Now, we calculate the area:
\[ A = \frac{1}{2} \times 64 \times 16 = 32 \times 16 = 512 \text{ cm}^2 \]

### Final Answer
The area of the trapezium is \( 512 \text{ cm}^2 \).

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