The cross-section of a canal is in the shape of a trapezium and the area of cross-section is `360m^(2)`. If the canal is 12 m wide at the top and 8 m wide at the bottom the depth of the canal is :

Options

A. 36 m
B. 180 m
C. 45 m
D. none of these

Answer

To find the depth of the canal, we will use the formula for the area of a trapezium. The area \( A \) of a trapezium is given by the formula:

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

where:
- \( b_1 \) is the length of the top base,
- \( b_2 \) is the length of the bottom base,
- \( h \) is the height (or depth in this case).

### Step 1: Identify the given values
From the problem, we have:
- Area \( A = 360 \, m^2 \)
- Top base \( b_1 = 12 \, m \)
- Bottom base \( b_2 = 8 \, m \)

### Step 2: Substitute the values into the area formula
We can substitute the known values into the area formula:

\[ 360 = \frac{1}{2} \times (12 + 8) \times h \]

### Step 3: Simplify the equation
First, calculate the sum of the bases:

\[ 12 + 8 = 20 \]

Now, substitute this back into the equation:

\[ 360 = \frac{1}{2} \times 20 \times h \]

### Step 4: Multiply both sides by 2 to eliminate the fraction
\[ 720 = 20 \times h \]

### Step 5: Solve for \( h \)
Now, divide both sides by 20:

\[ h = \frac{720}{20} = 36 \]

### Conclusion
The depth of the canal is \( 36 \, m \).