In many parts of the world, kite flying is a popular pastime during the off-season of winter. Do you ever wonder how big it is, or how big the shovel that we use in our garden is compared to the one we use for gardening? Trapeziums are geometrical figures with four-sized, flat, two-dimensional sides and any single pair of opposite sides that are parallel to one another on all four sides.
Trapeziums are formed by the parallel sides known as the bases, while the non-parallel sides are known as the legs. The trapezoid shape is often referred to as the trapezoid shape. Now that we have discussed how the area of a trapezium can be calculated, let us take a look at what its different properties are.
Let’s Calculate Area of Trapezium
As a rule of thumb, the area of a trapezium can be calculated as follows: Area = 12 Sum of the lengths of the parallel sides of the trapezium Perpendicular distance between the parallel sides.
I would like to know how to find the area of a trapezium, if the bases of a kite are 10 and 15 inches and the height is 22 inches, for example.
Using the area of the trapezium, we will be able to find the answer:
The area of the trapezium is calculated as follows: 12(10+15)(22) = 275 square inches
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Types of trapeziums
Trapezium can be mainly classified into three types:
1. Right Trapezium
2. Isosceles Trapezium
3. Scalene Trapezium
In general, trapeziums can be categorized based on the length of the legs and/or the measurement of their angles, or both. As well as the formula for calculating the area of a trapezium, it also differs depending on what kind of trapezium it is. In order to understand its types, let us take a closer look at them:
Right Trapezium
Right trapeziums are trapezoids which are made up of two pairs of right angles that are adjoined to each other on both sides.
Isosceles Trapezium
As the name implies, an isosceles trapezium is a trapezium that has equal length non-paraallel sides or legs.
Scalene Trapezium
It is a trapezium in which all of the four sides have different measurements in relation to each other. A scalene trapezium also consists of different measures for all the angles on its surface.
Properties of a Trapezium
Every geometrical figure has a unique set of properties of its own, which serve to distinguish it from other geometrical figures while at the same time allowing it to be recognized from other geometrical figures. By using these properties, we can gain a better understanding of the different figures and make a better comparison between them in a detailed and rational manner. There are several properties of trapezium that can be found in the following table:
- 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 the 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, the diagonals of an isosceles trapezium are equal.
- The base angles of an isosceles trapezium are equivalent in measurement.
- In an 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 an 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.
Some Fun Facts About Trapezium
- The term trapezium comes from the Greek word “trapezion” which translates to “a little table” in English.
- A trapezium is a group of stars in the Orion Nebula that is known as a group of stars. Our wrist also has a bone called the trapezium, which is also known as the trapezium bone.
- In real life, trapeziums can be found in a variety of things including tables, lamps, paper boats, shovels, popcorn tubs, flowerpots, handbags, and many others.
In a fun and interesting way, you can learn everything you need to know about trapeziums and their properties at Cuemath if you are interested in learning more.
