What is Trapezoid?
A trapezoid, also known as a trapezium, is a flat closed shape having 4 straight sides, with one pair of parallel sides.
The parallel sides of a trapezium are known as the bases, and its non-parallel sides are called legs. The parallel sides can be horizontal, vertical or slanting.
The perpendicular distance between the parallel sides is called the altitude.
Examples:
Non-Examples:
| (A) It is not a trapezoid because it is a 6-sided figure. | (B) It is not a trapezoid because it is a 3-sided figure with no parallel sides. |
| (C) It is not a trapezoid because it is a curved figure. | (D) It is not a trapezoid because it has rounded corners and 2 pairs of parallel sides. |
Begin here
Trapezoid Definition
- Exclusive Definition: A trapezoid is a quadrilateral with exactly one pair of parallel sides. (By this definition, a parallelogram is not a trapezoid since it has two pairs of parallel sides.)
- Inclusive Definition: A trapezoid is a quadrilateral with at least one pair of parallel sides. (By this definition, a parallelogram becomes a special type of trapezoid, a trapezoid with two pairs of parallel sides.)
Types of Trapezoid
Trapezoid is of three types namely
1. Right trapezoid: It has a pair of right angles.
2. Isosceles trapezoid: It has equal length of non-parallel sides. In the image, sides, AD and BC are equal.
3. Scalene trapezoid: It neither has equal angles nor has equal sides.
Median of Trapezoid
A median of a trapezoid is the line segment joining the midpoints of the two non-parallel sides of a trapezoid.
The median of a trapezoid is parallel to the set of parallel lines.
Median = $\frac{BC+AD}{2}$ = $\frac{a+b}{2}$
Properties of a Trapezoid
- The bases are parallel to each other.
- The median is parallel to both the bases and its length will be the average of the length of the bases.
- Sum of all the angles in a trapezoid is equal to 360°.
- The sum of the angles on the same side is equal to 180°.
Area of Trapezoid
Area of a trapezoid = $\frac{1}{2}$ × (sum of parallel sides) × (distance between them)
Let ABCD be a trapezoid in which AB is parallel to DC and let h be the height.
Area = $\left\{\frac{1}{2}\times (AB + BC)\times h \right\}$
= $\left\{\frac{1}{2}\times (a + b)\times h \right\}$
Perimeter of Trapezoid
The perimeter of a trapezoid is the sum of all its sides.
Therefore, for the trapezoid shown above with sides AB, BC, CD and DA, the perimeter can be written as
Perimeter = AB + BC + CD + DA
Real Life Examples
We can find trapezoids in many real-life objects For example a lamp, popcorn box, handbag, and so on.
Solved Examples on Trapezoid
Example 1: Fill in the blanks.
- The trapezoid having non-parallel sides equal is known as ______________.
- _____________ trapezoid has a pair of adjacent angles equal to 90°.
- Neither the sides nor the angles of _______________ trapezoid are equal.
Solution:
- isosceles trapezoid
- Right
- scalene
Example 2: Find the length of median PQ of given trapezoid.
Solution:
Median = $\frac{1}{2}\times (\text{sum of the basis}) = \frac{AD + BC}{2} = \frac{8 + 30}{2} cm = 19 cm$
Example 3: Find the perimeter of a given trapezoid.
Solution:
Perimeter = PQ + QR + RS + SP = (15 + 6 + 20 + 5) cm = 46 cm
Example 4: Find the area of a given trapezoid.
Solution:
Area = $\frac{1}{2}\times (\text{sum of parallel sides})\times (\text{altitude})$
= $\frac{1}{2}\times (7 + 11)\times 6$ sq.cm
= $\frac{1}{2}\times 18\times 6 sq.cm$
= 54 sq.cm
Practice Problems On Trapezoid
Trapezoid
The altitude refers to what measurement of a trapezoid?
The height of the trapezoid is referred to as it's altitude.
How many right angles are there in the right trapezoid?
A right trapezoid is a trapezium with a pair of right angles.
What is the difference between a trapezoid and a parallelogram?
Trapezoid has 1 pair of parallel sides and parallelogram has 2 pairs of parallel sides.
Both trapezoid and parallelogram are quadrilaterals. The difference lies in the number of parallel sides they have.
What do we call sides which are not parallel in a trapezoid?
The two parallel sides of the trapezoid are referred to as the bases of the trapezoid; the other two sides are called the legs of the trapezoid.
Frequently Asked Questions On Trapezoid
Are all trapezoids quadrilaterals?
Trapezoids are closed figures with 4 sides. So we can call them quadrilaterals.
What is the difference between a trapezoid and a trapezium?
What we call a trapezoid in the US is a trapezium in the UK. By the exclusive definition, both trapezoid (US) and trapezium (UK) are quadrilaterals with one pair of parallel sides. (Also, note that a quadrilateral with no parallel sides is called a trapezium in the US and a trapezoid in the UK.)
Can a trapezoid have 4 right angles?
No, a trapezoid can have either 2 right angles or no right angles at all.
Are all rhombuses also trapezoids?
- Under the exclusive definition, a trapezoid is a quadrilateral with only one pair of parallel sides. Thus, a rhombus which has two pairs of parallel sides, is not a trapezoid.
- Under the inclusive definition, a trapezoid has at least one pair of parallel sides. By this definition, a rhombus is a trapezoid.
Is trapezoid a parallelogram?
- By the exclusive definition, a trapezoid is not a parallelogram. Under this definition, a trapezoid has exactly one pair of parallel sides, while in a parallelogram, there are two pairs of parallel sides.
- By the inclusive definition, a trapezoid has at least one pair of parallel sides. Thus, when a trapezoid has two parallel sides, it becomes a parallelogram.
