Find the area of a trapezium whose parallel sides are 9 cm and 6cm respectively and the distance between these sides is 8 cm.

Answer

To find the area of a trapezium with parallel sides of lengths 9 cm and 6 cm, and a distance (height) of 8 cm between these sides, we can 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 (AB) = 9 cm
- Side 2 (CD) = 6 cm
- The height (distance between the parallel sides) is given as:
- Height (h) = 8 cm

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

### Step 3: Substitute the values into the formula
- Here, \(a = 9\) cm, \(b = 6\) cm, and \(h = 8\) cm.
- Substitute these values into the formula:
\[ A = \frac{1}{2} \times (9 + 6) \times 8 \]

### Step 4: Calculate the sum of the parallel sides
- Calculate \(9 + 6\):
\[ 9 + 6 = 15 \]

### Step 5: Substitute the sum back into the area formula
- Now substitute back into the area formula:
\[ A = \frac{1}{2} \times 15 \times 8 \]

### Step 6: Calculate the area
- First, calculate \(15 \times 8\):
\[ 15 \times 8 = 120 \]
- Now divide by 2:
\[ A = \frac{120}{2} = 60 \text{ cm}^2 \]

### Conclusion
The area of the trapezium is \(60 \text{ cm}^2\).

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