It’s the 2D geometry-enclosed space. A trapezium is a two-dimensional shape that belongs to the quadrilateral family. It has its properties and calculations based on area and perimeter, just as other geometrical shapes. The area of trapezoid in a two-dimensional plane is the area covered by a trapezium.

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## What is a Trapezium?

A trapezium is a quadrilateral, which has four sides and one set of parallel sides. There are four other forms of quadrilaterals besides the trapezium. They are as follows:

- Parallelogram
- Rectangle
- Square
- Rhombus

All these quadrilaterals have one common and similar property, that is, the total sum of all the angles is 360 degrees.

## The Composition of a Trapezium:

- The bases of the trapezoid are the pair of parallel sides, while the non-parallel sides are recognized as the legs.
- The mid-segment of a trapezoid is the line segment connecting the midpoints of the non-parallel sides.
- You must have known about the composition of isosceles triangles, where the two sides of a triangle are similar and the angle opposite to the equal sides are also equivalent. In the same order, we have a shape that is recognized as an Isosceles Trapezium, in which the two non-parallel sides are equal and form equal angles at one of the bases of the trapezium.
- Examine the various varieties of trapezium figures given on the Cuemath website, where the arrow symbolizes the parallel side. The two sides of each of the three figures are parallel to each other, however, the other two sides are not. Cuemath is an excellent online learning platform that makes learning engaging and interesting.
- The trapezium will be separated into two unequal pieces if a line segment is drawn between the two non-parallel sides from the mid-point of both sides.

## Properties of a Trapezium

Below are a few essential properties that are going to make learning easy and simple. A trapezium is also named and often termed as a trapezoid. A trapezium has the following characteristics:

- Like any other quadrilaterals in geometry, the total sum of all the four angles of the trapezium is equal to 360 degrees.
- Any given trapezium has two parallel sides and two non-parallel sides in its composition.
- The diagonals of regular trapezium bisect each other in the center.
- The length of the mid-segment is similar to half the sum of the parallel bases in the given trapezium.
- Two pairs of adjacent angles in a trapezium that forms between the parallel sides and one of the non-parallel side, invariably add up to 180 degrees.

## Area of a Trapezium

Trapezium area can be obtained by using the below-expressed formula: Area = (1/2) h (AB+CD)

### Derivation of Area of a Trapezium Formula:

The following is the root for expressing the area of a trapezoid:

The area of a trapezoid is similar to the total sum of the areas of the two triangles and the area of the rectangle as well.

We know from the above discussion that: area of trapezoid is equal to, area of triangle 1 + area of rectangle + area of triangle 2.

Which gives us,

A = (ah/2) + b1h + (ch/2) = (ah + 2b1h + ch)/2

Further simplifying the above equation, rearranging the terms in order, and factoring gives us:

A = h/2[b1 + (a + b1 + c)] ….(i)

If we imagine that the longer base of the trapezoid will be b2, then

b2 = a + b1 + c …..(ii)

Substituting the (ii) with the equation (i),

A = h/2(b1 + b2)

Therefore, the area of a trapezoid with bases b1, b2, and altitude h formula is;

A = h/2(b1+b2)

## Application of the Trapezium Formula:

The notion is often applied in physics calculations and other mathematical calculations. As explained in the 9th CBSE science textbook, this is the foundation for getting the equations of motion. The combination of physics equations and mathematical calculations is very carefully described in order to give a better perspective to the students.