If the lengths of the two parallel sides of a trapezium are 5 cm and 7 cm and the distance between these parallel sides is 4cm. Find its area (in `cm^(2)`).

Options

A. 12
B. 24
C. 48
D. 36

Answer

To find the area of the trapezium, we will 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 distance between the parallel sides.

### Step-by-Step Solution:

**Step 1: Identify the lengths of the parallel sides and the height.**
- Given \( a = 5 \, \text{cm} \) (length of one parallel side)
- Given \( b = 7 \, \text{cm} \) (length of the other parallel side)
- Given \( h = 4 \, \text{cm} \) (distance between the parallel sides)

**Step 2: Substitute the values into the area formula.**
\[ \text{Area} = \frac{1}{2} \times (5 + 7) \times 4 \]

**Step 3: Calculate the sum of the parallel sides.**
\[ 5 + 7 = 12 \]

**Step 4: Substitute the sum back into the area formula.**
\[ \text{Area} = \frac{1}{2} \times 12 \times 4 \]

**Step 5: Calculate the area.**
- First, calculate \( \frac{1}{2} \times 12 \):
\[ \frac{1}{2} \times 12 = 6 \]
- Then, multiply by the height \( 4 \):
\[ 6 \times 4 = 24 \]

**Final Answer:**
The area of the trapezium is \( 24 \, \text{cm}^2 \).

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