The two parallel sides of a trapezium are 16 m and 20 m respectively, and the perpendicular distance (height) between them is 10 m. What is the area of this trapezium in square metres?

Introduction / Context:
This mensuration problem involves a trapezium, a quadrilateral with exactly one pair of parallel sides. The area formula for a trapezium uses the average of the parallel sides multiplied by the height. Such questions check whether you can recall and correctly apply this basic area formula.

Given Data / Assumptions:

• Lengths of the parallel sides are 16 m and 20 m.
• The height (perpendicular distance between the parallel sides) is 10 m.
• We are asked for the area in square metres.
• The shape is a standard trapezium with one pair of parallel sides only.

Concept / Approach:
The area A of a trapezium with parallel sides a and b, and height h, is: A = (1/2) * (a + b) * h This formula can be seen as taking the average of the two bases and multiplying by the height, analogous to the base–height formula of a rectangle.

Step-by-Step Solution:
Let a = 16 m, b = 20 m, and h = 10 m. Compute a + b = 16 + 20 = 36. Apply the formula A = (1/2) * (a + b) * h. So A = (1/2) * 36 * 10. (1/2) * 36 = 18, so A = 18 * 10 = 180 square metres.

Verification / Alternative check:
You can think of the trapezium as a combination of a rectangle and two right triangles. Its average base length is (16 + 20)/2 = 18 m. If you imagine a rectangle of base 18 m and height 10 m, its area is 180 m², matching our trapezium area formula result.

Why Other Options Are Wrong:
260, 240, and 360 all arise from misusing the formula, such as forgetting the factor 1/2, adding height incorrectly, or multiplying the bases incorrectly. None of these match the proper computation using the trapezium area formula.

Common Pitfalls:
A frequent mistake is to multiply just one base by the height, as if the figure were a rectangle, or to take the difference of the bases instead of the sum. Remember always to add the lengths of the parallel sides, divide by 2, and then multiply by the height.

Final Answer:
The area of the trapezium is 180 m².