Correct Answer - Option 4 : 15 cm

**Given:**

Ratio of Parallel sides = 3 ∶ 5

Area of trapezium = 240 cm^{2}

Height of trapezium = 12 cm

**Concept**:

Replace the ratio with a constant and using the formula for the area of the trapezium, calculate the sides of the trapezium.

**Formula used:**

Area of trapezium = 1/2 × (Sum of parallel sides) × height

**Calculation:**

Let the parallel sides be 3x and 5x

Area of trapezium = 1/2 × (Sum of parallel sides) × height

⇒ 240 cm^{2} = 1/2 × (3x + 5x) × 12 cm

⇒ 240 cm^{2} = (1/2) × (8x) × 12 cm

⇒ 8x = (240 × 2)/12 cm

⇒ x = 40/8 cm

⇒ x = 5 cm

Shorter parallel side of the trapezium = 3x = 3 × 5 cm = 15 cm.

**∴ ****Shorter parallel side of the trapezium is 15 cm.**