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# what is a 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. 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:

## 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.

1. The trapezoid having non-parallel sides equal is known as ______________.
2. _____________ trapezoid has a pair of adjacent angles equal to 90°.
3. Neither the sides nor the angles of _______________ trapezoid are equal.

Solution:

1. isosceles trapezoid
2. Right
3. 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