## 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. |

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## 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.)*

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## 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.

**F**requently 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.