100 LearnersLast updated on August 13th, 2025
Properties of Trapezium
A trapezium is a type of quadrilateral that has unique properties. These properties help students simplify geometric problems related to trapeziums. The properties of a trapezium include having at least one pair of parallel sides. These properties help students to analyze and solve problems related to symmetry, angles, and area. Now let us learn more about the properties of a trapezium.
What are the Properties of a Trapezium?
The properties of a trapezium are simple, and they help students to understand and work with this type of quadrilateral. These properties are derived from the principles of geometry. There are several properties of a trapezium, and some of them are mentioned below: Property 1: One pair of parallel sides A trapezium has at least one pair of opposite sides that are parallel. Property 2: Non-parallel sides The other two sides of a trapezium are not necessarily equal or parallel. Property 3: Angles The sum of the angles in a trapezium is always 360 degrees. Property 4: Symmetry A trapezium can be isosceles, which means the non-parallel sides are equal in length, giving it a line of symmetry. Property 5: Area Formula The formula used to calculate the area of a trapezium is given below: Area = ½ × (a + b) × h Here, 'a' and 'b' are the lengths of the parallel sides, and 'h' is the height.
Tips and Tricks for Properties of a Trapezium
Students tend to confuse and make mistakes while learning the properties of a trapezium. To avoid such confusion, we can follow the following tips and tricks: One Pair of Parallel Sides: Students should remember that in a trapezium, at least one pair of opposite sides is parallel. To verify this, students can draw a trapezium and see that two sides are parallel. Isosceles Trapezium: Students should remember that an isosceles trapezium has equal non-parallel sides, which can aid in solving symmetry-related problems. Area Calculation: Students should practice using the area formula for a trapezium: Area = ½ × (a + b) × h, to ensure they understand how to apply it correctly.
Confusing a Trapezium with a Rectangle
Students should remember that a trapezium has only one pair of parallel sides, whereas a rectangle has two pairs of parallel sides.
Mistake 1
Misinterpreting the Angle Sum
Students should know and remember that the sum of all interior angles in any quadrilateral, including a trapezium, is always 360 degrees.
Mistake 2
Incorrectly Applying the Area Formula
Students should practice the formula used to find the area of a trapezium, which is given below. The students must also understand the representations of 'a', 'b', and 'h'. Area = ½ × (a + b) × h
Mistake 3
Misunderstanding Parallel Side Relationships
Students should remember that a trapezium must have exactly one pair of parallel sides, unlike other quadrilaterals like parallelograms which have two pairs.
Mistake 4
Forgetting the Non-parallel Side Rule
Students must remember that in a trapezium, the non-parallel sides are not necessarily equal, except in the case of an isosceles trapezium.
Mistake 5
Solved Examples on the Properties of Trapeziums
In a trapezium, the parallel sides are marked as AB and CD. If AB = 6 cm, CD = 10 cm, and the height is 4 cm, what is the area of the trapezium?
Area = 32 sq cm.
Problem 1
Applying the formula, Area = ½ × (a + b) × h Substituting the values into the formula, we get: Area = ½ × (6 + 10) × 4 = 32 cm².
In a trapezium ABCD, if angle ABC = 120 degrees and angle BCD = 80 degrees, what is the measure of angle DAB?
Explanation
Angle DAB = 80 degrees.
Problem 2
The sum of the angles in a trapezium is 360 degrees. So, angle DAB + angle ABC + angle BCD + angle CDA = 360 degrees. Given angle ABC = 120 degrees and angle BCD = 80 degrees, and assuming angle DAB = angle CDA (for simplicity in an isosceles trapezium), angle DAB = 80 degrees.
If the non-parallel sides of an isosceles trapezium are equal, and one angle is 70 degrees, what is the measure of the angle adjacent to it?
Explanation
The adjacent angle is 110 degrees.
Problem 3
In an isosceles trapezium, the base angles are equal, and the consecutive angles between the parallel sides are supplementary. If one angle is 70 degrees, the adjacent angle must be 110 degrees (since 70 + 110 = 180 degrees).
In trapezium ABCD, parallel sides AB and CD are 8 cm and 12 cm respectively. If the height is 5 cm, find the area of trapezium.
Explanation
Area = 50 sq cm.
Problem 4
Using the area formula, Area = ½ × (a + b) × h Substituting the values, Area = ½ × (8 + 12) × 5 = 50 cm².
A trapezium has an area of 60 cm², and its height is 6 cm. If one of the parallel sides is 5 cm, find the length of the other parallel side.
Explanation
The other parallel side is 15 cm.
A trapezium is a quadrilateral that has at least one pair of opposite sides that are parallel.
1.How many pairs of parallel sides does a trapezium have?
2.Are all sides of a trapezium equal?
3.How do you find the area of a trapezium?
4.Can a trapezium have all four sides equal?
Common Mistakes and How to Avoid Them in Properties of Trapeziums
Students tend to get confused when understanding the properties of a trapezium, and they tend to make mistakes while solving problems related to these properties. Here are some common mistakes the students tend to make and the solutions to said common mistakes.
Hiralee Lalitkumar Makwana
About the Author
Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.
Fun Fact
: She loves to read number jokes and games.
