Trapezium — Area is 384 sq cm. Parallel sides are in ratio 3 : 5 and the distance between them (height) is 12 cm. Find the smaller parallel side.

Introduction / Context:
The area of a trapezium (trapezoid) equals 1/2 * (sum of parallel sides) * height. If the parallel sides are in ratio 3 : 5, we can express them as 3x and 5x and solve for x from the area relation.

Given Data / Assumptions:

• A = 384 sq cm
• Height h = 12 cm
• Parallel sides = 3x and 5x

Concept / Approach:
Use A = (1/2)(a + b)h = (1/2)(3x + 5x) * 12 = (1/2)(8x) * 12 = 48x.

Step-by-Step Solution:
48x = 384 ⇒ x = 8Smaller side = 3x = 3 * 8 = 24 cm

Verification / Alternative check:
Area check: (1/2)(24 + 40) * 12 = (1/2)(64) * 12 = 32 * 12 = 384 ✔

Why Other Options Are Wrong:
20, 30, and 36 cm do not satisfy the exact ratio/area; 18 cm uses x = 6, not consistent with A = 384.

Common Pitfalls:
Mixing up which side is smaller; forgetting to halve the sum in the area formula.

Final Answer:
24 cm