The cross-section of a canal is a trapezium in shape . If the canal is 20 m wide at the to pand 12 m wide at the bottom and the area of the cross-section is 640 sq m, find the length of the cross-section.

Options

A. 80 m
B. 40 m
C. 60 m
D. 70 m

Answer

To solve the problem step by step, we will use the formula for the area of a trapezium.

### Step 1: Understand the dimensions of the trapezium
The trapezium has two parallel sides:
- The top width (a) = 20 m
- The bottom width (b) = 12 m

### Step 2: Write down the formula for the area of a trapezium
The area (A) of a trapezium is given by the formula:
\[ A = \frac{1}{2} \times (a + b) \times h \]
where:
- \( a \) = length of the top side
- \( b \) = length of the bottom side
- \( h \) = height of the trapezium (which we need to find)

### Step 3: Substitute the known values into the formula
We know the area \( A = 640 \, \text{sq m} \), \( a = 20 \, \text{m} \), and \( b = 12 \, \text{m} \). Substituting these values into the formula gives:
\[ 640 = \frac{1}{2} \times (20 + 12) \times h \]

### Step 4: Simplify the equation
First, calculate \( (20 + 12) \):
\[ 20 + 12 = 32 \]
Now substitute this back into the equation:
\[ 640 = \frac{1}{2} \times 32 \times h \]

### Step 5: Multiply both sides by 2 to eliminate the fraction
\[ 640 \times 2 = 32 \times h \]
This simplifies to:
\[ 1280 = 32h \]

### Step 6: Solve for \( h \)
Now, divide both sides by 32 to find \( h \):
\[ h = \frac{1280}{32} \]
Calculating this gives:
\[ h = 40 \, \text{m} \]

### Step 7: Conclusion
The height of the trapezium (length of the cross-section of the canal) is \( 40 \, \text{m} \).

### Final Answer
The length of the cross-section is **40 meters**.

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