The area of a trapezium is the space occupied by a two-dimensional shape with four sides, where the lengths of the parallel sides are different. The formula for finding the area of a trapezium is given by:

Area = (a + b) × h / 2

Where "a" and "b" are the lengths of the parallel sides, and "h" is the height or perpendicular distance between the parallel sides.

The area of a trapezium has various real-life applications such as in construction, architecture, and engineering. For example, the shape of a trapezium is commonly used in the design of roofs, where the roof has two parallel sides of different lengths, and the height of the roof represents the perpendicular distance between the two parallel sides. The area of a trapezium is also used in calculating the volume of containers or tanks that have trapezoidal cross-sections.

The formula for determining the area of a trapezium/trapezoid is defined as:

\(A\) \(=\) \(\dfrac{a + b}{2}\) \(\cdot\) \(h\)

\(A\): the area of the trapezium

\(a\): the length of the shorter base

\(b\): the length of the longer base

\(h\): the length of the height

The SI unit of area is: \(square \text{ } meter\text{ }(m^2)\)