A trapezium has two parallel sides of lengths 12 cm and 10 cm. The perpendicular distance (height) between these parallel sides is 14 cm. Find the area of the trapezium in sq cm using the standard trapezium area formula.

Introduction / Context:
This question tests the standard area formula of a trapezium (also called a trapezoid in some regions). A trapezium has exactly one pair of parallel sides. The area is the average of the lengths of the parallel sides multiplied by the perpendicular distance between them. Since the sides and height are given directly, it is a straightforward substitution problem.

Given Data / Assumptions:

• Parallel side a = 12 cm
• Parallel side b = 10 cm
• Height h (distance between parallel sides) = 14 cm
• Area formula: area = (1/2) * (a + b) * h

Concept / Approach:
Add the two parallel sides, take half of that sum (which represents the average base length), then multiply by the height. Keep everything in cm so the final unit is sq cm.

Step-by-Step Solution:

Verification / Alternative check:
The average of 12 and 10 is 11, so area should be close to 11 * 14 = 154. This is also between the areas of rectangles 10*14=140 and 12*14=168, which makes sense because a trapezium with bases 10 and 12 must have area between those two rectangle areas. Hence 154 is consistent.

Why Other Options Are Wrong:

Common Pitfalls:
Common mistakes include forgetting the 1/2 factor, multiplying the two bases directly, or using non-perpendicular distance as height. Another frequent error is treating the trapezium like a triangle with base 12 and height 14, which ignores the second parallel side of length 10.

Final Answer:
154 sq cm