The altitude of a trapezium whose area is 105 `cm^2` and base are 14 cm and 7 cm is `h` cm. The value of `h` is

Answer

To find the altitude (height) \( h \) of the trapezium, we can use the formula for the area of a trapezium:

\[ \text{Area} = \frac{1}{2} \times (b_1 + b_2) \times h \]

where \( b_1 \) and \( b_2 \) are the lengths of the two parallel sides (bases) and \( h \) is the height.

### Step 1: Identify the given values
- Area = \( 105 \, \text{cm}^2 \)
- Base 1 (\( b_1 \)) = \( 14 \, \text{cm} \)
- Base 2 (\( b_2 \)) = \( 7 \, \text{cm} \)

### Step 2: Write the formula for the area of the trapezium
Using the area formula:

\[ 105 = \frac{1}{2} \times (14 + 7) \times h \]

### Step 3: Calculate the sum of the bases
Calculate \( b_1 + b_2 \):

\[ b_1 + b_2 = 14 + 7 = 21 \, \text{cm} \]

### Step 4: Substitute the sum of the bases into the area formula
Now substitute this value back into the area formula:

\[ 105 = \frac{1}{2} \times 21 \times h \]

### Step 5: Simplify the equation
Multiply both sides by 2 to eliminate the fraction:

\[ 210 = 21 \times h \]

### Step 6: Solve for \( h \)
Now, divide both sides by 21 to isolate \( h \):

\[ h = \frac{210}{21} \]

### Step 7: Calculate the value of \( h \)
Perform the division:

\[ h = 10 \, \text{cm} \]

Thus, the value of \( h \) is \( 10 \, \text{cm} \).

---