The space or region which is covered by the sides of trapezium in a plane that is two-dimensional is known as the area of trapezium. A trapezium can be defined as a type of quadrilateral which is two-dimensional and measured in unit square. As every other shape in geometry, it also has its own property and formulas for area and perimeter. Basically, a trapezium is made up of four sides, one parallel and the other nonparallel to each other. The area of trapezium depends on the height of the trapezium. Mathematically, we can write area is equal to ½ * a+b *h where ‘h’ can be regarded as the height of the sides which are parallel whereas ‘a’ and ‘b’ are the height of the sides which are parallel to each other.

## Properties of Trapezium

As mentioned, trapezium is one of the shapes that come in geometry which has four sides, one parallel and the other nonparallel to each other. A trapezium is also known as the trapezoid. The properties of a trapezium are very diverse, approximately there are more than 4 basic properties of it. In the next few paragraphs, we may deal with the properties of a trapezium. When we talk about a trapezium, we must not forget to deal with its application, as it is widely used in mathematical and physical calculations.

## Formula of Area of Trapezium Along with Some Calculations

The area of trapezium is the region or space covered by the parallel and nonparallel sides of the trapezium. If we define the area mathematically, the area given for a trapezium is ½ * h * a+b where ‘h’ is the height of the parallel sides and ‘a’ and ‘b’ are the length/distance of sides which are parallel. Let us try to solve some examples in order to understand this topic in a better way.

Example 1:

Calculate the area of trapezium if the length of parallel sides is equal to 5 cm and 10 cm and the given height is 4 cm?

Provided that,

Length of parallel sides = a; 5cm and b; 10cm

Height of parallel sides = 4cm

Using the formula of the Area of Trapezium, ½ * h * a+b,

½ * 4 *( 5 + 10 )= 30 cm square units.

Hence, the area of trapezium is equal to = 30 cm square units.

Example 2:

Calculate the area of trapezium if the length of parallel sides is equal to 8cm and 10 cm and the given height is 4 cm?

Provided that,

Length of parallel sides = a; 8cm and b; 10cm

Height of parallel sides = 4cm

Using the formula of the Area of Trapezium, ½ * h * a+b,

½ * 4 * (8 + 10) = 36 cm square units.

Hence, the area of trapezium is equal to = 36 cm square units.

## Detailed Analysis Of Properties Of Trapezium

The following points mentioned below analyses the properties of trapezium. Some of them are as follows:

- In a trapezium, you will find the sides of it to be both parallel and nonparallel. In simple words, one pair of sides are parallel to each other.
- The diagonals of a trapezium intersect each other.
- As mentioned, trapezium has both parallel and nonparallel sides. The nonparallel sides of the trapezium are not equal. Exception: Isosceles Trapezium.
- The sum of the angles interior to the sides of a trapezium gives us a value of 360 degrees which basically signifies each angle measures about 90 degrees.
- The adjacent angles of the trapezium are supplementary which means, they give a value equal to 180 degrees.

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