The shape of the cross section of a canal is a trapezium. If the canal is 10 m wide at the top, 6 m wide at the bottom and the area of its cross section is 640 `m^(2)`, find the depth of the canal.

Explanation

To find the depth of the canal whose cross-section is a trapezium, we can use the formula for the area of a trapezium. The area \( A \) of a trapezium can be calculated using the formula:

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

where \( b_1 \) and \( b_2 \) are the lengths of the two parallel sides, and \( h \) is the height (or depth, in this case).

### Given:
- Width at the top \( b_1 = 10 \, m \)
- Width at the bottom \( b_2 = 6 \, m \)
- Area \( A = 640 \, m^2 \)

### Step 1: Substitute the known values into the area formula

We can substitute the values of \( b_1 \), \( b_2 \), and \( A \) into the area formula:

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

### Step 2: 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 3: Multiply both sides by 2 to eliminate the fraction

\[ 1280 = 16h \]

### Step 4: Solve for \( h \)

Now, divide both sides by 16:

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

Calculating this gives:

\[ h = 80 \, m \]

### Conclusion

The depth of the canal is \( 80 \, m \).

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