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Trapezoids are defined as quadrilaterals that have two parallel sides. It is a four-sided closed 2D figure or shape that has a perimeter and area. The length of the two parallel sides of a trapezoid is different and the other two sides are non-parallel. The parallel sides of a trapezoid are known as bases, whereas the non-parallel sides of a trapezoid are known as lateral sides or legs. Altitude is defined as the distance between two parallel sides.
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Keyterms: Quadrilaterals, Trapezoid, Right Trapezoids, Isosceles Trapezoids, Scalene Trapezoids, Curve
Also Read: Remainder Theorem
Types of Trapezoids
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A trapezoid is divided into three types which are mentioned in the below points:
- Right Trapezoids
- Isosceles Trapezoids
- Scalene Trapezoids
Right Trapezoids
Right Trapezoids have a set of two right angles. It is also known as a right-angled trapezoid. To estimate areas under the curves, these types of trapezoids are used.
Right Trapezoid
Isosceles Trapezoids
If the length of legs of a trapezoid or the non-parallel sides is equivalent, then it is termed as Isosceles Trapezoids. The measure of both base angles and legs are similar in Isosceles Trapezoids. In isosceles trapezoids, the angles of parallel sides i.e., base are equal to each other. It has a line of symmetry and the length of both the diagonals are equivalent.
Isosceles Trapezoid
Scalene Trapezoids
Scalene Trapezoids are a type of trapezoids in which neither the angles nor the sides of a trapezium are equivalent.
Scalene Trapezoids
Shapes of Trapezoids
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The shape of trapezoids is a four-sided shape. It has one pair of sides which is parallel. A trapezoid is primarily a two-dimensional figure or shape that is similar to a rectangle, square, and parallelogram. Therefore, this shape has are and perimeter as other shapes have.
Also Read: Area of a Trapezoid Formula
Area of Trapezoids
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By taking the two base averages and multiplying them with altitude, the area of a trapezoid is calculated. Given below, the formula for the area of trapezoids:
Area of Trapezoid
Area of Trapezoids (A) = 1/2 x (Sum of Parallel Sides) x (Distance Between Them).
Area = 1/2 x (a + b) x h
where, 'a' and 'b' = base.
h = height or distance or altitude between parallel lines.
Perimeter of Trapezoids
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The sum of all the sides of a trapezoid is the perimeter of a trapezoid. If the four sides of a trapezoid is a, b, c, d, then the formula of the perimeter will be,
Perimeter (P) = a + b + c + d
Also Read: Perimeter of a Parallelogram
Properties of Trapezoids
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The properties of Trapezoids are mentioned in the below points:
- The top and bottom of the bases are parallel to each other.
- The length of the opposite sides of a trapezoid i.e., isosceles are similar.
- To both the bases, the median is parallel.
- Two pairs of adjacent angles sum up to 180°
- The length of the medians is the average of both the top and bottom bases i.e., (a + b)/2
- A trapezoid is said to be a rectangle if both the pairs of the opposite sides are parallel and the length of the opposite side are equivalent and at right angles to each other.
- A trapezoid is said to be a parallelogram if, in a trapezoid, the two pairs of the opposite sides are parallel.
- A trapezoid is said to be a square, if the length of all sides is equivalent, two pairs of the opposite sides are parallel, and at right angles to each other.
- The joining points of the diagonals are collinear to the center of both the pairs of opposite sides.
- The line that connects the center of the non-parallel sides is always parallel or to the bases which are equivalent to half the sum of the parallel sides.
Also Read:
| Unit Related Topics | ||
|---|---|---|
| Area of Rectangle | Areas of Parallelograms and Triangles Important Theorems | Area of Parallelogram |
| Trapezoid Formula | Perimeter of a Trapezoid | Parallelogram Area |
Things to Remember
- Trapezoids is a four-sided closed 2D figure or shape that has a perimeter and area.
- Bases are known as the parallel sides of a trapezoid are known as bases.
- The non-parallel sides of a trapezoid are known as lateral sides or legs.
- A trapezoid is divided into three types- Right Trapezoids, Isosceles Trapezoids, Scalene Trapezoids.
- A trapezoid is primarily a two-dimensional figure or shape that is similar to a rectangle, square, and parallelogram.
Sample Questions
Ques. What is the other name of Trapezium in some parts of the world? (1 Mark)
Ans. The other name of Trapezium in some parts of the world is Trapezoid.
Ques. What is irregular trapezium? (1 Mark)
Ans. Irregular trapezium is defined as a trapezium in which the non-parallel opposite sides are unequal.
Ques. How the unit of an area of trapezium is measured? (1 Mark)
Ans. The unit of an area of trapezium is measured in square units like square feet, square inches, square meters, etc.
Ques. What is the difference between trapezium and trapezoid? (1 Mark)
Ans. The difference between trapezium and trapezoid is that trapezoid is a four-sided polygon that has no pair of parallel sides opposite to each other, whereas trapezium is a four-sided polygon that has one pair of parallel sides opposite to each other.
Ques. Mention three attributes of trapezoids? (2 Marks)
Ans. The three attributes of trapezoids are:
- The diagonals and the base angles are equal in an isosceles trapezoid.
- The joining points of the diagonals are collinear to the center of both the pairs of opposite sides.
- In an isosceles trapezoid, the lengths of the opposite sides are congruent or similar to each other.
Ques. Find out the area of a trapezium, in which the sum of the base is 40 cm and height is 10 cm. (3 Marks)
Ans. Given, Sum of the base (a+b) = 40 cm
Height (h) = 10 cm,
We know that,
Area of Trapezoids (A) = 1/2 x (Sum of Parallel Sides) x (Distance Between Them)
A = 1/2 x (a + b) x h
A = 1/2 x (40 cm) x 10 cm
A = 200 cm2.
Hence, the Area of the Trapezium is 200 cm2.
Example 1: Find the Perimeter of Trapezium ABCD whose Side Measures are 12 cm, 14 cm, 16cm, and 18 cm. (3 Marks)
Solution: Given, a = 12 cm, b = 14 cm, c = 16 cm, d = 18 cm
We know that, Perimeter of Trapezium = Sum of its all four sides.
Perimeter = a + b + c + d
P = 22 + 16 + 13 + 8
P = 59 cm
Hence, the Perimeter of a Trapezium is 59 cm.
Ques. Mark True or False for below statements: (3 Marks)
(a) If two triangles area are same areas, they will be congruent
(b) Two triangles having the same base (or equal bases) and equal areas lie between the same parallels.
(c) The area of a triangle is equal to the product of any of its side and any altitude
(d) The median of the triangles divides the triangle into two triangles of equal areas
(e) Parallelograms on the same base and between same parallels have same perimeter
(f) In a parallelogram, diagonals divide the parallelogram into four equal triangles
Ans. (a) False. Congruent triangles have equal areas but converse is not true
(b) True. Triangle area is (1/) X base X height. With same base and area, height should be equivalent, which means they lie on same parallel
(c) False. It is corresponding base and corresponding altitude
(d) True.
(e) False. Area is same but perimeter can be different
(f) True
Ques. PQRS is a quadrilateral whose diagonal bisect each other at right angles (3 Marks)
a) PQRS is a Square
b) PQRS is a rectangle
c) PQRS is a rhombus
d) None of these
Ans. Solution (c)
Ques. In the given figure ABCD is a parallelogram AE ⊥ DC and CF ⊥ AD. If AB = 18 cm, AE = 8 cm and CF = 16 cm, find AD. (3 Marks)
a) 9 cm
b) 8 cm
c) 10 cm
d) None of the above
Ans. (a) Parallelogram area= base X height
So DC×AE=AD×CF
Or AD=DC×AE/CF=9 cm
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