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Trapezium -Definition, Properties, Types and Area
Trapezium
Definition:-A trapezium is a type of quadrilateral (2D shape) in which two opposite sides are parallel and two opposite sides are not parallel .Parallel sides are referred as the bases and non-parallel sides are known as the legs of the Trapezium.
A convex Quadrilateral with at least single pair of parallel sides is known as Trapezium in English outside North America . And Trapezium is also known as a Trapezoid in American and Canada English.
Properties of Trapezoid:-
Basic properties of Trapezoid are stated below.
- One pair of opposite side is parallel.
- Consecutive angles are supplementary. i.e. <A+<D=180° .
- The line that joins the mid point of two non parallel sides is always parallel to the base of the trapezium (mid-segment=(AB+CD) /2).
- Sum of the internal angles is 360°.
Types of Trapezium/Trapezoid
1.Right Trapezoid : –It is a type of Trapezoid having two right angles.
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| Trapezium -Definition, Properties, Types and Area |
2.Isosceles Trapezium :- It is a type of Trapezoid in which base angles are equal and therefore non- parallel sides left and right are also equal.
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| Trapezium -Definition, Properties, Types and Area |
3.Scalene Trapezoid:–It is a type of Trapezoid which has neither equal angles nor equal sides.
Area Of Trapezoid
How to find the Area of Trapezium(samlamb chaturbhuj).
Below figure ABCD is a Trapezium in which AC diagonal creates two triangles in it.
If we able to find the area of two triangles ,then we also able to find the area of Trapezium by adding two areas of triangles.
△ACD and △ABC are two triangles.
Area of triangle △ACD= 1/2*h*CD .
Area of triangle △ABC = 1/2*h*AB .
Area of Trapezoid ABCD = Area of triangle △ACD + Area of triangle △ABC
= 1/2*h*CD + 1/2*h*AB
=1/2*h(CD+AB).
=1/2*h*(AB+CD) —-is the Area of Trapezoid ABCD
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| Trapezium -Definition, Properties, Types and Area |
Example: Find the Area of Trapezoid whose parallel sides are 120 m. and 75m. respectively.
And distance between two parallel lines is 58m.
Ans- Area of Trapezoid = 1/2(sum of parallel sides)*distance between them.
= 1/2*(120+75)*58.
=1/2*195*58
=5655 sq. meter.
Example:-How many sides of a Trapezium(Trapezium ke kitne side hote hai) ?
Answer:- There are four sides of a Trapezium as it is a type of Quadrilateral. A trapezium is a type of quadrilateral (2D shape) in which two opposite sides are parallel and two opposite sides are not parallel .
Perimeter Of Trapezoid
Perimeter of a Trapezoid = sum of all four sides.
Example : Find the Perimeter of Trapezoid whose parallel sides are 120 m. and 75m. respectively and non-parallel sides are 105 meters and 72 meters.
Ans-As we know the Perimeter of Trapezoid is the sum of all four sides.
Perimeter of a Trapezoid = 120+75+105+72= 372 meters.
Real Life Examples of Trapezoid shaped objects
- Table top
- Pop corn Tub
- Handbags
- Doors and Windows
- Flower base
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| Trapezium -Definition, Properties, Types and Area |
Frequently Asked Questions:
1.What is a Trapezium Shape?
Ans– A trapezium is a type of quadrilateral (2D shape) in which two opposite sides are parallel and two opposite sides are not parallel .
2.How many types of trapezium are there?
Ans–Trapezoid is of Three types mainly
- right Trapezoid
- isosceles Trapezoid
- scalene Trapezoid
3.Does a trapezium have equal sides?
Ans– yes. Isosceles Trapezium is a type of Trapezoid in which base angles are equal and therefore non- parallel sides left and right are also equal.
4.Can a trapezoid have two right angles?
Ans-yes. Right Trapezoid is a type of Trapezoid having two right angles.
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