The length of two parallel sides of a trapezium are 15 cm and 20 cm. If its area is 175 sq. cm, then its height is :

Options

A. 15 cm
B. 10 cm
C. 20 cm
D. 25 cm

Answer

To find the height of the trapezium given the lengths of its parallel sides and its area, 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:
- Length of the first parallel side \( a = 15 \) cm,
- Length of the second parallel side \( b = 20 \) cm,
- Area = 175 sq. cm.

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

\[ 175 = \frac{1}{2} \times (15 + 20) \times h \]

### Step 2: Simplify the expression inside the parentheses.

\[ 15 + 20 = 35 \]

So the equation becomes:

\[ 175 = \frac{1}{2} \times 35 \times h \]

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

\[ 2 \times 175 = 35 \times h \]

\[ 350 = 35h \]

### Step 4: Solve for \( h \) by dividing both sides by 35.

\[ h = \frac{350}{35} \]

### Step 5: Simplify the division.

\[ h = 10 \, \text{cm} \]

Thus, the height of the trapezium is **10 cm**.

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