The area of a trapezium is 18 sq. cm. Its height and base are 3 cm and 5 cm respectively. Find the length of the side parallel to the base.
A. 4 cm
B. 6 cm
C. 8cm
D. 7 cm

Options

A. A
B. B
C. D
D. C

Answer

To solve the problem, we will use the formula for the area of a trapezium, which is given by:

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

where:
- \( a \) is the length of the side parallel to the base,
- \( b \) is the length of the base,
- \( h \) is the height of the trapezium.

Given:
- Area = 18 sq. cm
- Height (\( h \)) = 3 cm
- Base (\( b \)) = 5 cm

We need to find the length of the side parallel to the base (\( a \)).

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

\[ 18 = \frac{1}{2} \times (a + 5) \times 3 \]

### Step 2: Simplify the equation

Multiply both sides by 2 to eliminate the fraction:

\[ 36 = (a + 5) \times 3 \]

### Step 3: Divide both sides by 3

\[ 12 = a + 5 \]

### Step 4: Solve for \( a \)

Subtract 5 from both sides:

\[ a = 12 - 5 \]

\[ a = 7 \text{ cm} \]

### Conclusion

The length of the side parallel to the base is \( 7 \) cm. Therefore, the correct answer is option D.

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