A trapezium has two parallel sides of lengths 18 m and 24 m, and its height is 12 m. What is the area of the trapezium in square metres?

Introduction / Context:
This is a straightforward mensuration question on the area of a trapezium. Trapeziums appear regularly in aptitude tests, and knowing the basic area formula saves time and avoids confusion with rectangles or triangles.

Given Data / Assumptions:
• The two parallel sides of the trapezium are 18 m and 24 m. • The perpendicular distance between these parallel sides (height) is 12 m. • We are asked to find the area in square metres.

Concept / Approach:
The area A of a trapezium with parallel sides a and b and height h is given by A = (1 / 2) * (a + b) * h. This formula can be remembered as the average of the parallel sides times the height. Here, the parallel sides are 18 m and 24 m, and the height is 12 m, so we simply substitute these values into the formula.

Step-by-Step Solution:
1. Let a = 18 m and b = 24 m be the lengths of the parallel sides. 2. Let h = 12 m be the height of the trapezium. 3. Use the trapezium area formula: A = (1 / 2) * (a + b) * h. 4. Compute a + b = 18 + 24 = 42 m. 5. Multiply by the height: (a + b) * h = 42 * 12 = 504 square metres. 6. Now multiply by 1 / 2: A = (1 / 2) * 504 = 252 square metres.

Verification / Alternative check:
You can think of the area as the average of the two bases times the height. The average of 18 m and 24 m is (18 + 24) / 2 = 42 / 2 = 21 m. Multiplying this by the height 12 m gives 21 * 12 = 252 square metres, which matches our earlier calculation. This alternative perspective confirms the result.

Why Other Options Are Wrong:
• 126 sq.m: This corresponds to taking half of the correct area and arises if you mistakenly divide twice by 2. • 504 sq.m: This is the value before multiplying by 1 / 2, so it ignores the full trapezium formula. • 1024 sq.m: This is unrelated to the given numbers and likely a distractor. • 378 sq.m: This does not follow from any reasonable combination of the sides and height.

Common Pitfalls:
Many students confuse the trapezium formula with triangle area, or forget the 1 / 2 factor entirely. Others mistakenly use only one base instead of the sum. Always recall that a trapezium can be thought of as having an effective base equal to the average of the two parallel sides.

Final Answer:
The area of the trapezium is 252 sq.m.