(i) Area of triangle `= (1)/(2)xx(…..)xx(…..)`.
(ii) Area of `a||gm=(1)/(2)xx(……)xx(……)`.
(iii) Area of a trapezium `=(1)/(2)xx(……)xx(……)`.
(iv) The parallel sides of a trapezium are 14 cm and 18 cm and the distance between them is 8 cm. The area of the trapezium is ……. `cm^(2)`.

Answer

To solve the question step by step, let's break it down into parts as outlined in the video transcript.

### Step-by-Step Solution:

**(i) Area of a Triangle:**
The formula for the area of a triangle is:
\[ \text{Area of Triangle} = \frac{1}{2} \times \text{base} \times \text{height} \]

**(ii) Area of a Parallelogram:**
The formula for the area of a parallelogram is:
\[ \text{Area of Parallelogram} = \text{base} \times \text{height} \]
(Note: The formula is simplified as the factor of 2 cancels out.)

**(iii) Area of a Trapezium:**
The formula for the area of a trapezium is:
\[ \text{Area of Trapezium} = \frac{1}{2} \times (\text{sum of parallel sides}) \times \text{height} \]

**(iv) Calculating the Area of the Trapezium:**
Given:
- Length of the first parallel side (a) = 14 cm
- Length of the second parallel side (b) = 18 cm
- Height (h) = 8 cm

1. **Calculate the sum of the parallel sides:**
\[ \text{Sum of parallel sides} = a + b = 14 \, \text{cm} + 18 \, \text{cm} = 32 \, \text{cm} \]

2. **Substitute the values into the trapezium area formula:**
\[ \text{Area of Trapezium} = \frac{1}{2} \times (\text{sum of parallel sides}) \times \text{height} \]
\[ = \frac{1}{2} \times 32 \, \text{cm} \times 8 \, \text{cm} \]

3. **Calculate the area:**
- First, calculate \( \frac{1}{2} \times 32 = 16 \, \text{cm} \).
- Then, multiply by the height:
\[ 16 \, \text{cm} \times 8 \, \text{cm} = 128 \, \text{cm}^2 \]

### Final Answer:
The area of the trapezium is \( 128 \, \text{cm}^2 \).

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