Geometry, the art of shapes and spaces, unveils the wonders of trapeziums, a four-sided figure with two parallel sides and two non-parallel sides. One of the fundamental aspects of exploring trapeziums lies in understanding their area—a measure that encapsulates the space they occupy on the geometric canvas.

Table of Contents

**What Is the Area of Trapezium?**

The area of a trapezium represents the space enclosed within its four sides. It is the magnitude of the region covered, providing a quantitative measure of the geometric entity. Calculating the area of a trapezium involves a formula that considers the lengths of its bases and the perpendicular distance between them.

## Area of Trapezium Formula

The formula to compute the area (A) of a trapezium is elegantly expressed as:

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

where:

- 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

The process of finding the area of a trapezium involves a systematic approach:

### 1. Identify the Bases

Recognize the two parallel sides of the trapezium, termed as bases.

### 2. Measure the Height

Determine the perpendicular distance (hh) between the bases. This is the height of the trapezium.

### 3. Apply the Formula

Utilize the area formula A = \(\frac{1}{2}h(a + b)\) , where aa and bb are the lengths of the bases.

### 4. Calculate

Perform the calculations to derive the numerical value of the trapezium’s area.

**Solved Examples on the Area of Trapezium**

**Example 1:Consider a trapezium with bases a = 8 units and b = 12 units. The height (h) measures 5 units.**

A = \(\frac{1}{2}(5)(8 + 12)\)

A =\(\frac{1}{2}(5)(20)\)

A = \(\frac{1}{2}(100)\)

A = \(50 \, \text{square units}\)

**Example 2:Imagine another trapezium with bases a = 10 units and b = 14 units. The height (h) is 6 units.**

A = \(\frac{1}{2}(6)(10 + 14)\)

A = \(\frac{1}{2}(6)(24)\)

Area of Trapezium = \(\frac{1}{2}(144)\)

A = \(72 \, \text{square units}\)

Here, the area of the trapezium is 72 square units.