Some Fun Facts About Trapezium

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Most of us fly kites during the offset of winters. Have you wondered about the size of it or about the size of the shovel that we use in our garden? It is a trapezium – a four sized, flat, two-dimensional geometrical figure with any single pair of opposite sides parallel to each other. Parallel sides of the trapezium are called the bases, while the non-parallel sides are called the legs. It is often known as trapezoid. We will now discuss how the area of a trapezium can be calculated and what are its various properties.

Let’s Calculate Area of Trapezium

The area of a trapezium can be calculated as follows: Area= ½ Sum of the length of its parallel sides Perpendicular distance between the parallel sides.

For Example: If the bases of a kite are 10 and 15 in and height is 22 in, how can we find the area of a trapezium?

We will use the area of trapezium to find it: 

Area of Trapezium = ½(10+15)(22) = 275 in^2

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Types of Trapeziums

Trapezium can be mainly classified into three types:

1. Right Trapezium

2. Isosceles Trapezium

3. Scalene Trapezium

Trapeziums are classified broadly on the basis of the length of the legs or the measurement of their angles. The formula of area of trapezium also differs according to the type of trapezium. Let us explore about its types in detail:

Right Trapezium 

A trapezium which has two pairs of right angles adjoining each other is known as right trapezium.

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Isosceles Trapezium

A trapezium that has legs or the non-parallel side of equal length is called an isosceles trapezium.

Scalene Trapezium

It is a trapezium in which all the four sides are different in measurement. All the angles of a scalene trapezium are also of different measures.

Properties of a Trapezium

Every geometrical figure has different properties of its own that distinguishes and at the same time makes it identifiable from other geometrical figures. These properties help us in understanding and making a comparison between the different figures in a well detailed manner. The various properties of trapezium are listed below:

  • It is a two-dimensional geometric figure.
  • It is a quadrilateral in which exactly one pair of opposite sides are parallel and the remaining two sides are non-parallel.
  • The sum of the interior angles of a trapezium is 360° while the sum of the angles of the adjacent sides of a trapezium is 180°.
  • In case of a trapezium, its diagonals will always bisect each other.
  • The non-parallel sides of a trapezium are unequal. However, there is an exception. Isosceles trapezium has equal non-parallel sides.
  • The legs of the non-parallel sides of an isosceles trapezium are congruent.
  • The diagonals of a trapezium are unequal. They always intersect with each other. However, diagonals of an isosceles trapezium are equal.
  • The base angles of an isosceles trapezium are equivalent in measurement.
  • In isosceles trapezium, the diagonals form two pairs of congruent triangles. One pair is an acute triangle while the other pair is an obtuse triangle.
  • In isosceles trapezium, the point of intersection of the diagonals lies on the diameter of the circumscribing circle.
  • In a circle, an isosceles trapezium can be inscribed.
  • If we rotate an isosceles trapezium about the vertical axis joining the mid-points of the parallel sides, what we get is a frustum of a cone.
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Some Fun Facts About Trapezium

  • Trapezium comes from the Greek word “trapezion” which translates to “a little table”.
  • A group of stars in the Orion Nebula is known as trapezium. There is a bone in our wrist which is also known as trapezium.
  • You can find real life examples of trapeziums in tabletops, lamps, paper boats, shovels, popcorn tub, flowerpot, handbags and so on.

If you want to learn more about trapezium and its properties in a fun and an interesting way, visit Cuemath.

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