The length of two parallel sides of a trapezium are 30 cm and 40 cm. If the area of the trapezium is 350 `cm^(2)` , then what is the value (in cm) of its height?

Options

A. 8
B. 10
C. 15
D. 12

Answer

To find the height 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 two parallel sides,
- \( h \) is the height.

**Step 1: Identify the values.**
- Length of the first parallel side \( a = 30 \, \text{cm} \)
- Length of the second parallel side \( b = 40 \, \text{cm} \)
- Area \( = 350 \, \text{cm}^2 \)

**Step 2: Substitute the values into the area formula.**
\[ 350 = \frac{1}{2} \times (30 + 40) \times h \]

**Step 3: Calculate the sum of the parallel sides.**
\[ 30 + 40 = 70 \]

**Step 4: Substitute the sum back into the equation.**
\[ 350 = \frac{1}{2} \times 70 \times h \]

**Step 5: Simplify the equation.**
\[ 350 = 35 \times h \]

**Step 6: Solve for \( h \).**
\[ h = \frac{350}{35} \]
\[ h = 10 \, \text{cm} \]

Thus, the height of the trapezium is \( 10 \, \text{cm} \).