Mensuration - Area of Trapezium and General Quadrilateral

A Trapezium is a quadrilateral with at least one pair of parallel sides, known as the bases. Visually, it appears as a four-sided figure where two sides run in the same direction but have different lengths, like the cross-section of a gold bar.

The height (h) or altitude of a trapezium is the perpendicular distance between its two parallel sides. In a diagram, this is often represented as a dashed line forming a $90^{\circ}$ angle with both parallel bases.

An Isosceles Trapezium is a special type where the non-parallel sides are equal in length. Visually, this shape is perfectly symmetrical along a vertical axis passing through the midpoints of the parallel sides.

A general quadrilateral can be divided into two triangles by drawing one of its diagonals. Visually, if you take any four-sided polygon and draw a line from one corner to the opposite corner (the diagonal $d$), you create two triangles sharing that diagonal as a common base.

Offsets in a general quadrilateral are the perpendiculars dropped from the remaining two vertices to the chosen diagonal. If the diagonal is $d$, the lengths of these two perpendicular lines are denoted as $h_{1}$ and $h_{2}$, effectively showing the 'height' of each constituent triangle.

The area of a general quadrilateral is the sum of the areas of the two triangles it is composed of. Visually, the total space inside the quadrilateral is filled by $\triangle 1$ with height $h_{1}$ and $\triangle 2$ with height $h_{2}$, both sharing base $d$.

A Rhombus is a quadrilateral where all sides are equal and diagonals bisect each other at right angles ($90^{\circ}$). Visually, it looks like a diamond shape where the two diagonals divide it into four identical right-angled triangles.

Area calculation often involves unit consistency. Ensure all measurements (cm, m, mm) are converted to the same unit before applying formulas to avoid calculation errors.