The cross section of canal is a trapezium in shape .If the canal is 10 metres wide at the top and 6 metres wide at bottom and the area of cross section is 640 sq. metres .The depth of canal is -----

Options

A. A)40 metres
B. B)80 metres
C. C)160 metres
D. D)384 metres

Answer

To find the depth of the canal, we can 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 dimensions
From the question, we have:
- \( b_1 = 10 \) meters (top width)
- \( b_2 = 6 \) meters (bottom width)
- \( A = 640 \) square meters (area)

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

\[ 640 = \frac{1}{2} \times (10 + 6) \times h \]

### Step 3: Simplify the equation
Calculate \( (10 + 6) \):

\[ 10 + 6 = 16 \]

Now, substitute this back into the equation:

\[ 640 = \frac{1}{2} \times 16 \times h \]

### Step 4: Multiply both sides by 2 to eliminate the fraction
Multiply both sides by 2:

\[ 1280 = 16h \]

### Step 5: Solve for \( h \)
Now, divide both sides by 16 to find \( h \):

\[ h = \frac{1280}{16} \]

Calculating this gives:

\[ h = 80 \text{ meters} \]

### Conclusion
The depth of the canal is \( 80 \) meters.

---