What is the formula for the area of a trapezium?

The area of a trapezium is defined by taking half the sum of the lengths of the two parallel sides (often referred to as the bases) and multiplying that sum by the height (the perpendicular distance between the bases). This formula effectively calculates the average length of the two bases and then multiplies this average by the height to find the enclosed area.

To clarify further, if we denote the lengths of the parallel sides as ( a ) and ( b ), and the height as ( h ), the area can be expressed as:

[ \text{Area} = \frac{1}{2} \cdot (a + b) \cdot h ]

This approach accounts for the trapezium's shape, as simply using the height multiplied by a base would not accurately capture the total area unless the trapezium were a rectangle. The other options represent different calculations that do not align with the trapezium's geometric properties. Thus, using the correct approach provides the area measurement that properly reflects the trapezium's dimensions.