A trapezium has two parallel sides of lengths 16 m and 20 m, and its height is 10 m. What is the area of the trapezium in square metres?

Introduction / Context:
This problem is a direct application of the formula for the area of a trapezium (also called a trapezoid in some regions). A trapezium is a quadrilateral with exactly one pair of opposite sides parallel. The area depends on the average of the lengths of the parallel sides multiplied by the height (the perpendicular distance between them). Here all necessary dimensions are provided, so the main task is to substitute correctly and simplify.

Given Data / Assumptions:

• The figure is a trapezium.
• The lengths of the two parallel sides are 16 m and 20 m.
• The height, or perpendicular distance between the parallel sides, is 10 m.
• We are asked to calculate the area in square metres.
• Standard geometric formulas for trapeziums apply.

Concept / Approach:
The area A of a trapezium with parallel sides of lengths a and b and height h is given by A = (1 / 2) * (a + b) * h. This can be understood as the average width of the parallel sides multiplied by the height. In this question, a = 16, b = 20, and h = 10, so we simply plug these values into the formula and compute the result.

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

Verification / Alternative check:
Another way to visualise the area is to see the trapezium as a rectangle plus two right triangles, or as the difference between a larger rectangle and two right triangles, depending on orientation. All such decompositions lead to the same effective formula: half the sum of parallel sides times height. Substituting 16, 20, and 10 consistently reproduces 180 sq m, confirming that our calculation is correct.

Why Other Options Are Wrong:
Option 360 would correspond to using (a + b) * h without multiplying by 1 / 2, overestimating the area by a factor of 2. Option 260 and 240 are arbitrary values that might result from incorrectly adding or averaging the sides. Option 200 might come from misusing only one side with the height. None of these follow the standard trapezium area formula with the given dimensions.

Common Pitfalls:
A common mistake is to forget the factor (1 / 2) and simply multiply (a + b) by h. Others may average the wrong pair of sides or confuse the height with one of the non parallel sides. Carefully identifying the parallel sides and using the correct formula with all factors included prevents such errors.

Final Answer:
The area of the trapezium is 180 square metres.