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Sets in Mathematics are the collection of definite objects that can form a group. The collection of numbers, days of the week, types of vehicles,...
Last Modified 11-04-2024
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April 11, 2024
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Trapezoid: Definition, Properties, Types & Solved Examples
Trapezoid: It is a convex quadrilateral shape consisting of one pair of parallel sides with four edges and vertices. The parallel sides of the trapezoid are called bases and the other sides are called legs. The distance between the parallel sides is known as height. In some regions, the trapezoid is also referred to as trapezium. There are different types of trapezoid such as right, scalene and isosceles. We can say that parallelogram is not a trapezoid as it consists of two opposite parallel sides.
The trapezoid is a two-dimensional polygon figure having its area and perimeter. This is one of the most important geometrical shapes in mathematics. It is also used in the field of architecture, engineering, science etc. Students learn trapezoid from an early age in order to solve mathematical problems in fractions of seconds. You can check NCERT Solution for Class 9 Maths Chapter 8 on quadrilaterals. We have provided detailed information on trapezoids in this article. Read on to find out about its definition, properties, types and examples.
Definition Of Trapezoid
The term trapezoid was derived from the Greek word Trapezoin meaning “a little table”. A Trapezoid is a convex quadrilateral consisting of one pair of opposite parallel sides. It is a two-dimensional figure with edges and vertices. The parallel sides of the trapezoid are called base and non parallel sides as legs. It is not necessary that parallel sides will be a straight line, as it can either be horizontal or slanting. The distance between the two parallel sides is called height or altitude.
The real life examples of trapezoid can be bridge, table, handbag etc. The trapezoid could have been a parallelogram if both pairs had parallel sides. And it could have called a square if both the sides were in equal length and rectangle if both the sides were parallel to each other.
Properties Of Trapezoid
Some of the properties of trapezoid are given below:
- It is a polygon
- It is two-dimensional figure similar to rectangle, square and parallelogram.
- It consists of four sides
- It consists of four edges and vertices
- It has supplementary adjacent angles.
- The mid points of sides are collinear to the intersection of diagonals.
- The diagonals of the trapezoid can be divided into the same ratio.
Types Of Trapezoid
The different types of trapezoid are mentioned below:
- Scalene Trapezoid: It has four unequal sides and angles. The bases are parallel to each other but with different lengths.
- Right Trapezoid: It has one pair of right angles between base and leg.
- Isosceles Trapezoid: The bases have unequal lengths whereas, the legs have equal length.
| Download NCERT Solutions for Class 9 Maths Chapter 8 PDF |
Area And Perimeter Of Trapezoid
The area of trapezoid is the average of pair of bases multiplied by height. It can be calculated by using the following formula:
| Area of Trapezoid = 1/2 (a + b) h |
Whereas, perimeter is the sum of all the sides. It can be calculated by using the following formula as mentioned below:
| Perimeter of Trapezoid= a + b + c + d |
Examples Of Trapezoid
Some of the examples of trapezoid are given below:
Example 1: Find the area of a trapezoid with bases of 4 meters and 6 meters and a height of 8 meters.
Solution: We know that the area of a Trapezoid is 1/2 (a + b)×h
Area=4+6/2×8m2
=Area=10/2×8m2
= 40 m2
Example 2: A trapezoid has four sides measuring 2m, 4m, 6m and 3m. Find its perimeter.
Solution: We know that Perimeter is given by Sum of all the sides.
Therefore, Perimeter = 2+4+6+3
= 15 m
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FAQs On Trapezoid
The frequently asked questions on trapezoid are given below:
| Q. What is trapezoid? A. It is a convex quadrilateral shape consisting of one pair of parallel sides with four edges and vertices. |
| Q. What are the types of trapezoid? A. The types of trapezoid are scalene, right and isosceles. |
| Q. Is parallelogram a trapezoid? A. Parallelogram is not a trapezoid as it consists of two opposite parallel sides. |
| Q. What is the area and perimeter of trapezoid? A. The area of trapezoid is the average of pair of bases multiplied by height. It is calculated by using the formula, 1/2(a +b) h. Whereas, the perimeter is the sum of all the sides. It is calculated by using formula a + b + c + d. |
Now that you have detailed information on trapezoid, practice all the questions at Embibe for better preparation. We hope this article on Trapezoid helps you. If you have any question then feel to post them here. We will get back to you at the earliest. Stay tuned to embibe.com for more updates.
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