1. Trapezium
A trapezium (or trapezoid in some countries) is a quadrilateral in which one pair of opposite sides is parallel. These parallel sides are called the bases of the trapezium.
A trapezium has four sides in total, but unlike rectangles or parallelograms, its sides are usually all different in length. Therefore, we cannot simplify its perimeter using a single compact formula involving repeated sides.
1.1. Definition of Perimeter
The perimeter of a trapezium is the sum of the lengths of all four sides. Since the sides usually differ, we simply add each side individually.
2. Perimeter Formula
If the four sides of a trapezium are \(a\), \(b\), \(c\), and \(d\), then the perimeter is calculated as:
\( P = a + b + c + d \)
3. Examples
Let’s look at a few examples to understand how to use the formula.
3.1. Example 1
A trapezium has side lengths \(a = 7\,\text{cm}\), \(b = 5\,\text{cm}\), \(c = 6\,\text{cm}\), and \(d = 4\,\text{cm}\). Its perimeter is:
\( P = 7 + 5 + 6 + 4 = 22\,\text{cm} \)
3.2. Example 2
A field in the shape of a trapezium has sides \(12\,\text{m}\), \(15\,\text{m}\), \(9\,\text{m}\), and \(11\,\text{m}\). The boundary length is:
\( P = 12 + 15 + 9 + 11 = 47\,\text{m} \)