Trapezium

A quadrilateral with only one pair of parallel sides is known as a trapezium. A trapezium is made up of two non-parallel sides called legs. The area of a trapezium is the amount of space it occupies on a two-dimensional plane. A trapezium is made up of four vertices and four angles.

The area of a trapezium is measured in square units, such as (cm², m², in²). Read the article to discover more about the trapezium formula, its derivation, and several examples.

Trapezium

A trapezium is a four-sided polygon with two pairs of parallel and non-parallel sides. Four vertices and four angles make up the trapezium. The trapezium’s parallel sides are called bases, while the non-parallel sides are called legs. A trapezoid is another name for a trapezium.

Area of Trapezium

The area of a trapezium figure in 2D space or the coordinate plane is the area covered by one of its faces. The figure’s two parallel sides, known as the bases, and the shape’s maximum height are used to compute the surface area. 

A direct perpendicular line is drawn from the peak of one base to the other to calculate the height. Pythagoras’ theorem is then used to determine the height of the trapezium (because the perpendicular makes a right-angle triangle). The formula for calculating the area of any trapezium object is:

Area of Trapezium=1 ⁄ 2(Sum of Parallel Sides) ×Distance between the Parallel Sides

A=1 ⁄ 2a+b×h

Here, a and b are the length of parallel sides and h is the distance between the parallel sides. 

Basic Terms of Trapezium

The Base of a Trapezium

The bases of a trapezium are the pair of parallel sides of a trapezium.

Height of a Trapezium

The height or altitude of a trapezium is defined as the perpendicular distance between its parallel sides.

Types of a Trapezium

Isosceles Trapezium

The non-parallel sides of an isosceles trapezoid are the same length as the parallel sides of a trapezium. The sum of all interior angles equals 360 degrees.

Scalene Trapezium

All of the sides and angles of a scalene Trapezium are of different sizes.

Right Trapezium

The Trapeziums are right Trapeziums if at least two of their angles are right angles.

Properties of a Trapezium                         

A trapezium is a four-sided shape. AB, BC, CD, DA are the sides of the trapezium ABCD

• A trapezium is made up of two pairs of parallel and non-parallel sides. AB and DC are parallel sides, however AD and BC are not
• A trapezium has four angles. Angles A, B, C, D are the four angles of a trapezium ABCD
• The sum of the four angles is 360 degrees (A+B+C+D=360 degrees)
• A+D=B+C=180o Is the sum of two pairs of neighboring angles of a trapezium produced between two parallel sides and one non-parallel side
• The isosceles trapezium’s legs are congruent
• Except in the isosceles trapezium, non-parallel sides are uneven
• The trapezium’s parallel sides are known legs, while the non-parallel sides are known bases

Perimeter of a Trapezium

The perimeter of a trapezium is equal to the sum of its sides. It is written mathematically as,

Perimeter of a trapezium ABCD=AB+BC+CD+DA.

Uses of a Trapezium

A trapezium is a polygon with four sides. A trapezium has numerous applications in our everyday lives. Trapezium shapes can be found on tabletops, bridge supporters, and architectural features, as well as in windows, doors, pencil boxes, and handbags.

In physics, the trapezium is used to address a variety of problems. Solving difficulties based on surface area or determining the area and perimeter of complex figures in mathematics. The trapezium formula is used in the construction of the roof’s shape. A trapezium is useful in a variety of situations.

Summary

A trapezium is a four-sided polygon with two pairs of parallel and non-parallel sides. The area of a trapezium is the area occupied by the trapezium on a two-dimensional plane. This article will teach you about trapeziums and their properties, as well as how to calculate the area of a trapezium formula. The trapezium formula is employed in the development of the roof’s shape.