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Trapezoid is a type of quadrilateral or polygon with 4 sides, in which at least two opposite sides are parallel to each other is known as Trapezoid or trapezium. The pair of sides in a trapezoid that is not parallel are called the legs of the trapezoid whereas the parallel sides are called the base of the trapezoid. The distance between the parallel lines is known as height.
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Key Terms: Perimeter, Trapezoid, Area, Perimeter of a Trapezoid, Base
Trapezoid
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A trapezium is also called trapezoid in American English, nonetheless, it is a quadrilateral having 4 sides which are called Edges, 4 corners which are called Vertices, and 4 angles.
In the above image,
- Edge of Trapezoid: AB, CD, BC, AD
- Vertices of Trapezoid: A, B, C, D
- Height of Trapezoid: a
- Base of Trapezoid: AB + CD
- Legs or Lateral sides of Trapezoid: AD +BC
Types of Trapezoids
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There are many types of trapezoids, here are the three mains:
- Right trapezoids – These are the trapezoids that have one pair of right angles between the base and the legs of the trapezoid.
Right trapezoids
- Scalene trapezoid – These are the trapezoids that have 4 unequal sides and angles. In these trapezoids, the bases are parallel to each other.
Scalene trapezoid
- Isosceles trapezoid- These are the trapezoids that have equal length of legs and unequal length of bases.
Isosceles trapezoid
Properties of Trapezoid
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- In an exact trapezoid only one pair of opposite sides or bases of a trapezoid is parallel to each other.
- In a trapezoid, the base is always parallel to the median.
- In a trapezoid diagonal always intersect each other.
- No parallel sides in a trapezoid are unequal except in the case of an isosceles trapezoid.
- In a trapezoid, the sum of interior angles is always 360.
- In a trapezoid, two adjacent angles are always supplementary.
Derivation of perimeter of Trapezoid Formula
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The total sum of all the four sides of a trapezoid is the perimeter of a trapezoid. On the other hand, in terms of Area, the perimeter of a trapezoid is calculated as
P= (total of lengths of non-parallel sides) + 2 A/H
In this A is the area of a trapezoid and H is the height of the trapezoid.
Perimeter of a trapezoid = AB + BC +CD +DA
Perimeter of a trapezoid = a + b + c + d
Important Definitions
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- Vertices: Vertices are the corners of a trapezoid.
- Lateral sides: There are four sides in a trapezoid, the sides which are non-parallel to each other are called the lateral sides or legs of the trapezoid.
- Bases: The sides of the trapezoid which are parallel to each other are called the bases.
Things to Remember
- There are two opposite sides in a trapezoid that are parallel to each other but it is not compulsory that the lengths of those sides are equal.
- There are mainly 4 variables in a trapezoid: height of a trapezoid, area of a trapezoid, and short base & long base of the trapezoid. In case any three of them are given the fourth variable could easily be found through the formula.
- The non-parallel sides of a trapezoid are called legs and the parallel sides are called the base.
Sample Questions
Ques. The sides of a tent are 12,24,36, and 29 cm respectively. What is the perimeter of that tent? (2 Marks)
Ans. Perimeter of a trapezoid – a+b+c+d=P
12+24+36+29 = 101 cm
The perimeter of that tent is 101 cm.
Ques. What is the perimeter of a trapezoid if a=2cm, b=4cm, c=6cm and d= 8cm? (2 Marks)
Ans. Perimeter of a trapezoid – a+b+c+d=P
2+4+6+8 = 20 cm
The perimeter of a trapezoid is 20 cm.
Ques. What would be the other side of a trapezoid if a= 3, b=4, c=8 and the perimeter of a trapezoid is 20. (2 Marks)
Ans. Perimeter of a trapezoid – a+b+c+d=P
3+4+8+d=20
15+d=20
d= 20-15
d= 5
The other side of a trapezoid is 5cm.
Ques. Two sides of the trapezoid are 6cm and 10 cm respectively and the other two sides are 5cm and 7 cm. What would be the perimeter of the trapezoid? (2 Marks)
Ans. Perimeter of a trapezoid – a+b+c+d=P
6+10+5+7= 28 cm
The perimeter of the Trapezoid is 28 cm.
Ques. What is the perimeter of a trapezoid if the units’ length is 12, 16, 18 and 22 units? (2 Marks)
Ans. Perimeter of a trapezoid – a+b+c+d=P
12+16+18+22 = 68 units
The perimeter of a trapezoid is 68 units
Ques. Is there any difference between trapezium and trapezoid? (2 Marks)
Ans. A quadrilateral or polygon with 4 sides that have at least one pair of opposite sides parallel to each other are called the trapezoid. In American English, it is called a trapezium. So, trapezoid and trapezium are both the same.
Ques. What are the types of Trapezoids? (2 Marks)
Ans. There are different types of Trapezoids. Three mains type of trapezoid are: -
- Right trapezoid- In this type of trapezoid, there is one right angle between the base and leg of a trapezoid.
- Scalene trapezoid – In this type of trapezoid, there are 4 unequal sides and angles only bases are parallel to each other.
- Isosceles trapezoid – In this type of Trapezoid, bases have unequal lengths and the length of legs are equal.
Ques.If the perimeter of a trapezoid is 64cm and the parallel sides are 15cm and 20 cm and assume the non-parallel sides are equal. What is the length of non-parallel sides? (3 Marks)
Ans. Perimeter of the trapezium= 64cm
Parallel sides are 15cm and 20cm.
Non-parallel sides are unequal.
Let those sides be x.
Formula P= a+b+c+d
64= 15+20+x+x
64= 35+ 2x
2x=64- 35
2x=29.
X= 29/2
X=14.5 cm
So, the length of non-parallel sides is 14.5 cm
Ques.The perimeter of a tent 30, 34, 46 and 56cm respectively. What would be the perimeter of the tent? (2 Marks)
Ans. Perimeter of the tent= a+b+c+d
30+34+46+56 =166 cm
The perimeter of the tent is 166cm .
Ques. What is the difference between a parallelogram and trapezoid? (2 Marks)
Ans. The difference between a parallelogram and a trapezoid is that a parallelogram has two pair of parallel side whereas the trapezoid always has one pair of parallel side
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