In the intricate world of geometry, trapeziums stand as versatile quadrilaterals with distinct characteristics, and understanding their area becomes a key pursuit. The area of a trapezium, essentially the space it occupies, is a geometric puzzle that can be solved with a thoughtful formula and a keen eye for measurements.

**What Is the Area of Trapezium?**

The area of a trapezium signifies the expanse within its four sides. It is a quantitative measure encapsulating the geometric magnitude of this quadrilateral. The calculation involves a formula that harmonizes the lengths of its bases and the perpendicular distance between them.

**Area of Trapezium Formula:**

The area formula for a trapezium is expressed as:

A = \(\frac{1}{2}h(a + b)\)

Here:

- h is the height, the perpendicular distance between the parallel bases,
- a and bb are the lengths of the two parallel bases.

**How to Find the Area of Trapezium**

Unlocking the area of a trapezium involves a systematic approach:

**Identify the Bases:**Recognize the two parallel sides of the trapezium, known as bases.**Measure the Height:**Determine the perpendicular distance (h) between the bases. This represents the height of the trapezium.**Apply the Formula:**Utilize the area formula A = \(\frac{1}{2}h(a + b)\), putting in the values for a, b, and hh.**Calculate:**Execute the mathematical operations to derive the numerical value of the trapezium’s area.

## Solved Examples on the Area of Trapezium

Let’s illuminate these theoretical concepts with diverse practical examples:

Example 1:Consider a trapezium with bases a = 12 units and b = 16 units. The height (h) measures 8 units.

A = \(\frac{1}{2}(8)(12 + 16)\)

A = \(\frac{1}{2}(8)(28)\)

A = \( \frac{1}{2}(224)\)

A = \(112 \, \text{square units}\)

In this instance, the area of the trapezium is =112 square units.

**Example 2:Imagine another trapezium with bases a=15 units and b=20 units. The height (h) is 10 units.**

A = \(\frac{1}{2}(10)(15 + 20)\)

A = \(\frac{1}{2}(10)(35)\)

A = \(\frac{1}{2}(350)\)

A = 1 \(75 \, \text{square units}\)

Here, the area of the trapezium is 175square units.