The area of a trapezium shaped field is `1920 m^(2)`, the height is 30 and one of the parallel sides is 40 m. Find the other parallel side.

Answer

To find the other parallel side of the trapezium-shaped field, we will use the formula for the area of a trapezium. The area \( A \) of a trapezium is given by:

\[ A = \frac{1}{2} \times (a + b) \times h \]

where:
- \( a \) and \( b \) are the lengths of the parallel sides,
- \( h \) is the height of the trapezium.

Given:
- Area \( A = 1920 \, m^2 \)
- Height \( h = 30 \, m \)
- One parallel side \( a = 40 \, m \)
- The other parallel side \( b = x \) (which we need to find)

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

\[ 1920 = \frac{1}{2} \times (40 + x) \times 30 \]

### Step 2: Simplify the equation.

First, multiply both sides by 2 to eliminate the fraction:

\[ 2 \times 1920 = (40 + x) \times 30 \]
\[ 3840 = (40 + x) \times 30 \]

### Step 3: Divide both sides by 30.

\[ \frac{3840}{30} = 40 + x \]
\[ 128 = 40 + x \]

### Step 4: Solve for \( x \).

Subtract 40 from both sides:

\[ 128 - 40 = x \]
\[ x = 88 \, m \]

### Conclusion:

The length of the other parallel side is \( 88 \, m \).

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