The area of a trapezium is 34 `cm^2` and the length of one of the parallel sides is 10 cm and its height is 4 cm. Find the length of the other parallel side.

Answer

To find the length of the other parallel side of the trapezium, we can use the formula for the area of a trapezium:

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

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

Given:
- Area \( = 34 \, \text{cm}^2 \)
- One parallel side \( a = 10 \, \text{cm} \)
- Height \( h = 4 \, \text{cm} \)
- The length of the other parallel side \( b = x \) (unknown)

We can substitute the known values into the area formula:

\[ 34 = \frac{1}{2} \times (10 + x) \times 4 \]

Now, let's simplify the equation step by step:

1. Multiply both sides by 2 to eliminate the fraction:

\[ 2 \times 34 = (10 + x) \times 4 \]

This simplifies to:

\[ 68 = (10 + x) \times 4 \]

2. Divide both sides by 4:

\[ \frac{68}{4} = 10 + x \]

This simplifies to:

\[ 17 = 10 + x \]

3. Now, isolate \( x \) by subtracting 10 from both sides:

\[ 17 - 10 = x \]

This gives us:

\[ x = 7 \]

So, the length of the other parallel side is \( 7 \, \text{cm} \).

### Final Answer:
The length of the other parallel side is \( 7 \, \text{cm} \).