PASSAGE-II : The area of trapezium equals half the sum of parallel sides multiplied by its height.
The altitude of a trapezium when, the sum of the lengths of whose parallel sides is 6.5 cm and whose area is 26 `cm^2` is

Options

A. 20 m
B. 4 cm
C. 6 cm
D. 8 cm

Answer

To solve the problem, we will use the formula for the area of a trapezium:

**Area of trapezium = (1/2) × (Sum of parallel sides) × Height**

Given:
- Area = 26 cm²
- Sum of parallel sides = 6.5 cm

We need to find the height (h).

### Step 1: Write down the formula for the area of a trapezium.
The formula is:
\[ \text{Area} = \frac{1}{2} \times (\text{Sum of parallel sides}) \times \text{Height} \]

### Step 2: Substitute the known values into the formula.
Substituting the given values into the formula:
\[ 26 = \frac{1}{2} \times 6.5 \times h \]

### Step 3: Simplify the equation.
To eliminate the fraction, we can multiply both sides of the equation by 2:
\[ 2 \times 26 = 6.5 \times h \]
\[ 52 = 6.5 \times h \]

### Step 4: Solve for h.
Now, we can isolate h by dividing both sides by 6.5:
\[ h = \frac{52}{6.5} \]

### Step 5: Calculate the value of h.
To simplify \( \frac{52}{6.5} \):
\[ h = \frac{52 \times 10}{65} = \frac{520}{65} \]
Now, divide 520 by 65:
\[ h = 8 \text{ cm} \]

### Final Answer:
The height (h) of the trapezium is **8 cm**.

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