Do you find maths interesting or boring? Everyone has different suggestions about this. Some feel maths is an easy and interesting subject but for some maths is difficult. Maths has different topics but the interesting topic is TRAPEZIUM. Many people feel a lot of difficulties while practicing this topic. Due to lockdown, it has become difficult for them to attend to their problems. So there is a solution for all the students who have problems while practicing maths. Let’s study briefly about trapezium and other concepts related to it.

Meaning Of Trapezium:- Trapezium is a space that is enclosed in 2D geometry with two-dimensional planes. It belongs to the family of quadrilaterals that have a 2D shape. Like the other geometrical shapes, it also has its properties and formulas.

Trapezium belongs to the family of quadrilaterals that have four sides and two parallel sides. Except for trapezium, four more shapes belong to the family of quadrilaterals.

- Rectangle
- Square
- Rhombus
- Parallelogram

The common thing in all the shapes that belong to the family of quadrilaterals is that the sum of their angles is 360°.

The basic concept gives us more detail about trapezium. The trapezium has a pair of parallel lines that are called bases. The other two left sides that are non-parallel are known as trapezoids. The line that connects the midpoint of the non-parallel lines is called the mid-segment. When you make a line from the midpoint of two unparallel lines then the trapezium is divided into unequal parts. There is a type of trapezium known as an isosceles trapezium, which means that non-parallel sides are equal and form equal angles at one of the bases.

**Properties of Trapezium:**

We have studied the basic concept of the trapezium. Now let’s go deep inside this topic and take the outlook on some of its properties. The properties of the trapezium are well known as trapezoids.

- Like other shapes that belong to the family of quadrilaterals, the sum of all angles is 360° in the trapezium.
- The shape of the trapezium depicts that it has two parallel sides and two non-parallel sides.
- Diagonals of the trapezium bisect each other.
- In trapezium, the mid-segment length is equal to half the sum of parallel bases.
- Two pairs of adjacent angles that formed between the parallel sides and the non-parallel sides have the sum 180°.

Area Of Trapezium:-

The formula used to calculate the area of trapezium is:

Area= (½) height (sum of parallel sides)

Let’s understand this formula with the assistance of an example:

> Find the area of trapezium if parallel sides are 4cm and 6cm resp. and the height of the trapezium is 3cm.

Ans- In question, we have given the length of two parallel sides that is 4cm and 6cm.

height = 3cm

The formula used to calculate area is:

Area= ½ × height ×( sum of parallel lines)

Area = ½ × 3× (4+6)

Area = ½ × 3× 10

Area = 1× 3× 5

Area = 15 cm²

So, the area of the trapezium is 15cm².

**Perimeter Of Trapezium:**

Like the area there is a formula to find the perimeter of the trapezium:

Perimeter = sum of all sides of a trapezium

Let’s understand it with the help of an example to get the proper knowledge about it.

> Calculate the perimeter of the trapezium if the parallel sides are 4cm and 10cm and non-parallel sides are 6cm and 8cm.

Ans:- Given,

parallel sides = 4cm and 10 cm

non-parallel sides = 6cm and 8cm

The formula wont to find the perimeter is:

Perimeter = sum of all the edges

Perimeter = 4+10+6+8

Perimeter = 28 cm

So, the perimeter of the trapezium is 28cm

So, these are the basic concepts that are studied under the topic trapezium. This concept is used in physics computations and mathematical calculations. For the engineering mind, this topic is a blend of both physics and mathematical calculations. The crucial part of this topic is the area of trapezium.

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