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What is Trapezoid? What are its properties and how does it look like? In geometry we go through several shapes with several dimensions and varying figures. Trapezoid is one of those found under the categories of Quadrilateral, which are known for having four sides. A trapezoid is a 2D figure which consists of four sides ‘AB, BC, BC, CD’ and also have at least one set of parallel sides which are opposite in nature.
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Key Terms: Trapiziod, Trapizium, Height of trapeziod, geometry, Quadrilateral, 2D figure, perpendicular height, short base, Longer base
Structure of Trapezoid
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Trapezoid is a form of quadrilateral, which means a figure with four sides. Among these four different sides, two opposite sides are parallel to each other with lengths being unequal. These two parallel sides are known as bases, ‘a shorter base’ and other being the ‘longer base’. The remaining sides are called legs and they are not parallel and might have equal or unequal lengths. The perpendicular height is known as altitude.
The video below explains this:
Trapezoid Formula Detailed Video Explanation:
Area of Trapezoid
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In order to determine the area of Trapezoid, one will need the lengths of shorter as well as longer base along with the attitude or height of the trapezoid.
Area of Trapezoid: a+b x h2
a = the short base
b = the longer base
h = height of the Trapezoid
In order to find the area of Trapezoid, one needs to follow the below mentioned steps:
- Add the two parallel bases ‘a’ and ‘b’
- Multiply the result with h (height of Trapezoid)
- Now divide the above task result with 2
- We will then get the area of Trapezoid.
Also Read:
Solved Examples for Area of Trapezoid
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Q1. Find the area of Trapezoid if the two bases are 5 and 6 cm. Also, the height is 4 cm.
Solution: Given: a = 5, b = 6, h = 4
Formula applied: a+b x h2
(5+6) x 42
= 11 x 4/2
= 22cm2
Q2. A trapezoid shorter base is 12 inches. The longer base is 28 inches, and the altitude is 6 inches. Determine the area of Trapezoid.
Solution: Given: a = 12, b = 28 and h = 6
Area of Trapezoid = a+b x h/2
(12 + 28) x 6/2
= 40 x 6/2
= 120 cm2
Height of Trapezoid
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There are questions which requires students to determine the height (h) of the trapezoid with providing the area and the length of the parallel sides. In such cases, one can follow the below mentioned formula:
Height of Trapezium: 2A / a +b
Where, A = Area of the Trapezium
And a and b are the longer and shorter bases.
Solved Examples for Height of Trapezoid
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Q1. A trapezoid have two parallel bases of length 5 and 6 respectively. The area of the Trapezoid is 22cm². Find the height of the trapezoid?
Solution: Given: a = 5, b = 6
Area of Trapezoid = 22cm2
Height of Trapezoid = 2 A / a +b
2 (22) / 5 + 6
= 44 / 11
= 4cm
If you have noticed, the same exact question is mentioned in the section of Area of Trapezoid examples. Hence, one can easily determine the height of Trapezoid if the area and the bases are given.
Q2. A corn field has a trapezoidal shape. The field has two parallel fences of 13 and 20 meters. If the area of the corn field is 2400 square meter, find the perpendicular distance between two parallel bases.
Solution: Given: a = 13, b = 20, Area = 2400
Using the formula: 2 A / a +b
= 2 (2400) / 13 + 20
= 145.45 m
Hence, the height of the trapezoid corn field is 145.45 meters.
Things to Remember
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Following are some important points:
- Trapezoids have two opposite sides parallel to each other however, this does not signify that their lengths will be equal.
- A trapezoid has four variables i.e., short base, long base, height or altitude and area of Trapezoid. If three variables are given, fourth can be determined by computing the main formula.
- Height of trapezoid is also known as altitude while the other two remaining sides who are not parallel are known as legs.
Also Read:
Sample Questions
Ques 1: What is a Trapezoid? (2 marks)
Ans: A trapezoid is a quadrilateral with at least two opposite sides parallel to each other. Hence, this four-sided polygon is a plane and closed object. It consists of four interior angles and four inner line segments. The parallel sides are known as bases and other two called legs.
Ques 2: How we can find the height of the Trapezoid? (3 marks)
Ans: Usually the Trapezoid mentions the height as well as lengths of the bases and one has to determine the area. However, in some cases one can be asked to find the height. A trapezoid has four variables, length of short base, length of longer base, height of Trapezoid and area of Trapezoid. If three variables are provided, we can easily calculate the fourth variable by rearranging the main formula which goes like:
Area of Trapezoid: a+b x h2
Height of Trapezoid: 2 A / a +b
Ques 3: What will be the area of Trapezoid if the two bases are 25 and 31 cm and height is 7 cm? (2 marks)
Ans: With the given information of a = 25, b = 31 and h = 7cm, one can compute the area of Trapezoid with the formula: a+b/h2
= (25 + 31) x 72
= 56 x 72
= 196 square cm
Ques 4: Find the height of Trapezoid if the area is 52 cm2 and the two parallel sides have length of 6 cm and 7 cm? (2 marks)
Ans: In such cases, we will use the formula after rearranging the actual formula of determining area which is: 2 A / a +b
= 2 multiplied by (A = area of trapezoid = 52) / 6 +7
= 104 / 13
= 8 cm
Ques 5: Is there any other types of Trapezoids? (2 marks)
Ans: Yes, there are different types of trapezoids such as Right Trapezoid, Isosceles Trapezoid, Scalene Trapezoid etc. A right trapezoid at least have two right angles in them. An Isosceles trapezoid have the two non-parallel sides of equal lengths. The trapezoid which have no sides of equal measure are known as Scalene Trapezoid.
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