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. A trapezium can also have parallel 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. |

## 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 = BC+AD2 = a+b2

## 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 = 12 × (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 = {12×(AB+BC)×h}

= {12×(a+b)×h}

**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 = 12×(sum of the basis)=AD+BC2=8+302cm=19cm

**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 = 12×(sum of parallel sides)×(altitude)

= 12×(7+11)×6 sq.cm

= 12×18×6sq.cm

= 54 sq.cm

## Practice Problems

1The altitude refers to what measurement of a trapezoid?HeighWidthAngleDiagonal2How many right angles are there in the right trapezoid?OneTwoThreeFour3What is the difference between trapezoid and parallelogram?Trapezoid has 2 pairs of parallel sides, and parallelogram has 1 pair of parallel sides.Trapezoid has 1 pair of parallel sides and parallelogram has 2 pairs of parallel sides.Trapezoid has 2 sides and parallelogram has 4 sides.Trapezoid has 4 equal angles and parallelogram has all 4 unequal angles.4What do we call sides which are not parallel in a trapezoid?Diagonals of trapezoidBases of trapezoidLegs of trapezoidAltitudes of trapezoid |