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## Trapezium

In geometry, There are many shapes whether it is two-dimensional or three-dimensional. But all the shapes or figures are distinct from one another by their special characteristics. Every shape, including the circle, square, rectangle, cylinder, sphere, and the list go on – has unique qualities and unique properties. The trapezium is one of the 2-dimensional shapes which is categorized into the quadrilateral category in geometry. In this article, we know about concepts, mathematical formulas, characteristics, and examples of the trapezium and solve some numerical problems based on Trapezium.

## Trapezium: Definition

The trapezium is a two-dimensional quadrilateral that has one pair of parallel opposite sides. A trapezium’s parallel and non-parallel sides are referred to as its bases and legs, respectively.

Although trapezium is a 2d dimensional figure, it is different from square and rectangle. Because trapezium has only one pair of parallel opposite sides whereas squares and rectangles have two pairs of parallel, equal opposite sides.

## Trapezium: Meaning in Hindi

समलम्ब चतुर्भुज एक द्वि-आयामी चतुर्भुज है जिसमें समानांतर विपरीत पक्षों की एक जोड़ी होती है। एक ट्रेपेज़ियम के समानांतर और गैर-समानांतर पक्षों को क्रमशः इसके आधार और पैर के रूप में जाना जाता है।

हालांकि समलम्ब चतुर्भुज एक 2d आयामी आकृति है, यह वर्ग और आयत से अलग है। क्योंकि समलम्ब चतुर्भुज में समानांतर विपरीत भुजाओं का केवल एक युग्म होता है जहाँ वर्गों और आयतों में समानांतर, समान विपरीत भुजाओं के दो जोड़े होते हैं।

जैसा कि हम पहले जानते हैं कि समलम्ब चतुर्भुज एक 2-आयामी तल पर चतुर्भुज आकार है, जो चार भुजाओं, चार कोनों और चार कोणों से बंद होता है। मूल रूप से, यदि हम किसी त्रिभुज के ऊपरी भाग को काटते हैं, तो यह एक समलम्ब चतुर्भुज जैसा दिखता है।

हम अपने दैनिक परिवेश में कई समलम्ब के आकार की वस्तुएँ देखते थे। हैंडबैग, ब्रिज ट्रस सपोर्ट, पॉपकॉर्न टिन, ट्रेपेज़ियम के आकार के खंभे, कूड़ेदान, कुछ गिटार आदि समलम्बाकार आकृतियों के कुछ उदाहरण हैं।

## Trapezium: Shape

As we know earlier trapezium is the quadrilateral shape on a 2-dimensional plane, closed with four sides, four corners, and four angles. Basically, if we cut the upper part of a Triangle, it looks like a trapezium.

We used to see many trapezium-shaped objects in our daily surroundings. Handbags, bridge truss supports, popcorn tins, trapezium-shaped pillars, Dustbins, some guitars etc, are a few examples of trapezoid shapes.

## Trapezium: Types

The trapezium is categorised into three types:

• Isosceles Trapezium

• Scalene Trapezium

• Right Trapezium

### Isosceles trapezium

Earlier know that Trapezium has two parallel sides (known as bases) and two non-parallel sides ( known as legs). If the legs or the non-parallel sides of the trapezium are equal in length, then the trapezium is called an isosceles trapezium.

### Scalene Trapezium

Scalene Trapeziums is formed when all the sides and angles of a trapezium have a different measurement or are unequal to each other.

### Right trapezium

A trapezium that has at least two adjacent right angles is referred to as a right trapezium.

## Irregular Trapezium

As we learn, a trapezium has one pair of parallel sides and two non-parallel sides. In a regular trapezium, the two non-parallel sides or legs are equal. Now, If a trapezium has unequal two non-parallel opposing sides, known as an irregular trapezium.

## Angle Trapezium

As a trapezium is a 2d quadrilateral thus it has four sides, four corners, and four angles. A quadrilateral that resembles a trapezoid has a total angle of 360°. Let assume,ABCD is a Trapezium. Then, ∠A+∠B+∠C+∠D = 360°.

•The total of the angles on two neighboring sides is 180°, which means that two angles on the same side are supplementary.

•The sum of four internal angles adds up to right angles, or 360°.

## Trapezium: Properties

The characteristics of every trapezium are as follows:

• A trapezium is a 2D quadrilateral which means it has four sides, four vertices, and four angles.

• In A trapezium two parallel sides are known as bases and the other two non-parallel sides are called legs.

• Trapezium has one set of opposite sides which is parallel to the other.

• The diagonals of the trapezium intersect each other and Both diagonals are the same length.

• The line connecting the non-parallel sides’ midpoints is always perpendicular to their bases, which is equal to half of the total number of parallel sides.

• In a trapezium, the sum of all four internal angles is always 360°.

• The total of the adjacent internal angles is 180°.

## Perimeter of trapezium

The total length of all the sides makes up the perimeter of a trapezium. Let’s assume ABC is a Trapezium that has four sides of length a, b, c, and d. Respectively. Consequently, the formula for a trapezium’s perimeter is

**Trapezium perimeter: P = a + b + c + d units**

## Trapezium Area formula

Trapezium area denotes the total area or places covered by that Trapezium. To determine the area of a trapezium we find the average of its two bases and multiply them by the height of the trapezium.

The formula for the area of the trapezium is as follows:

A trapezium’s area = h(a+b)/2 square units.

Where the length of two bases are “a” and “b” units and the length of the height is “h ” units.

## Trapezium formula

As we know that the Trapezium is a two-dimensional quadrilateral figure thus it has only two-dimensional quantities such as Area and perimeter. The formulas by which we can find out the area and perimeter are mentioned below.

Let’s suppose, ABCD is a Trapezium that has four sides of length a, b, c, and d. respectively. and the length of the height is “h ” units.

Area of Trapezium | ½ (Sum of parallel sides) (Distance between parallel sides) |

Perimeter of Trapezium | Sum of all four sides |

## Trapezium vs. Trapezoid

In mathematics meaning of both words, Trapezium and Trapezoid are the same. The trapezium is a four-sided polygon with exactly one pair of parallel sides that are opposite one another.

A trapezoid is a polygon with four sides that has one pair of parallel sides that are opposite one another.

But the two terms “trapezoid” and “trapezium” have different definitions in the US and the UK.

In the US, a quadrilateral that have one set of parallel sides is referred to as a trapezoid and a quadrilateral with no parallel sides is referred to as a trapezium.

In the UK, a quadrilateral having only one set of parallel sides is called a trapezium, whereas a quadrilateral with no parallel sides is called a trapezoid.

## Trapezium: Solved Examples

**Example 1: trapezium has the bases of 12 cm and 18 cm, respectively, and its height is 5 cm. Find the area of the trapezium.**

**Solution:**

As we know that the formula for determining the trapezium’s area is ((a+b)/2)h.

where the length of two bases are “a” and “b” units and the length of the height is “h ” units.

In the given problem,

The length of bases a is 12 cm, and b is 18 cm.

The length of the trapezium is (h)= 5 units.

So,

Area of trapezium = ((a+b)/2) h square units

= (12+18)/2) × 5 =(30/2) × 5 = 75 cm² .

E**xample 2:Determine the perimeter of the trapezium that has a length of the parallel sides are 10 cm and 12 cm respectively and the length of non-parallel sides is 5 cm each.**

**Solution :** As per given problem that a=11cm, b=13 cm, and c=d = 9 cm

We learn earlier that, the formula for a trapezium’s perimeter is

Trapezium perimeter: P = a + b + c + d units

Where the length of the four sides are a, b, c, and d cm respectively.

Perimeter of the given trapezium is P = a + b + c + d units

P = 11+13+9+9 cm

P= 42 cm (Answer)

## What is Trapezium : FAQs

**Q. What do you mean by trapezium?**

The trapezium is a two-dimensional quadrilateral that has one pair of parallel opposite sides. A trapezium’s parallel and non-parallel sides are referred to as its bases and legs, respectively.

**Q. What is isosceles trapezium?**

The trapezium has two parallel sides (known as bases) and two non-parallel sides ( known as legs). If the legs or the non-parallel sides of the trapezium are equal in length, then the trapezium is called an isosceles trapezium.

**Q.Is trapezium is a quadrilateral?**

Yes, The trapezium is a quadrilateral because it has four vertices and four sides that intersect at four distinct angles. Thus, a trapezium exhibits all the properties of a quadrilateral.

**Q. Write down five characteristics of a trapezium**.

A trapezium is a 2D quadrilateral which means it has four sides, four vertices, and four angles.

• In a trapezium, two parallel sides are known as bases and the other two non-parallel sides are called legs.

• Trapezium has one set of opposite sides which is parallel to the other.

• The diagonals of the trapezium intersect each other and Both diagonals are the same length.

• The line connecting the non-parallel sides’ midpoints is always perpendicular to their bases, which is equal to half of the total number of parallel sides.

• In a trapezium, the sum of all four internal angles is always 360°.

**Q. How to determine the area of a trapezium?**

The formula for the area of the trapezium is as follows:

A trapezium’s area = h(a+b)/2 square units.

Where the length of the two bases is “a” and “b” units and the length of the height is “h ” units.