Find the area of the trapezium whose parallel sides are 14cm and
10cm and whose height is 6cm.

Answer

To find the area of the trapezium with given parallel sides and height, we will follow these steps:

### Step 1: Identify the lengths of the parallel sides and the height.
- The lengths of the parallel sides are given as:
- Side 1 (a) = 14 cm
- Side 2 (b) = 10 cm
- The height (h) of the trapezium is given as:
- Height (h) = 6 cm

### Step 2: Use the formula for the area of a trapezium.
The formula for the area (A) of a trapezium is given by:
\[ A = \frac{1}{2} \times (a + b) \times h \]
Where:
- \( a \) and \( b \) are the lengths of the parallel sides,
- \( h \) is the height.

### Step 3: Substitute the values into the formula.
Now, we substitute the values of \( a \), \( b \), and \( h \) into the formula:
\[ A = \frac{1}{2} \times (14 \, \text{cm} + 10 \, \text{cm}) \times 6 \, \text{cm} \]

### Step 4: Calculate the sum of the parallel sides.
First, calculate \( a + b \):
\[ a + b = 14 \, \text{cm} + 10 \, \text{cm} = 24 \, \text{cm} \]

### Step 5: Substitute the sum back into the area formula.
Now, substitute \( 24 \, \text{cm} \) back into the formula:
\[ A = \frac{1}{2} \times 24 \, \text{cm} \times 6 \, \text{cm} \]

### Step 6: Calculate the area.
Now, calculate the area:
\[ A = \frac{1}{2} \times 24 \times 6 = 12 \times 6 = 72 \, \text{cm}^2 \]

### Final Answer:
The area of the trapezium is \( 72 \, \text{cm}^2 \).

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