# Trapezoid

## What is a Trapezoid?

A trapezoid, sometimes known as a trapezium, is a quadrilateral or four-sided polygon. It has a set of parallel opposing sides and a set of non-parallel sides. More so, The trapezoid’s parallel sides are known as the bases, while the non-parallel sides are known as the legs.

## Definition of Trapezoid

A trapezoid is a four-sided closed two-dimensional shape with a perimeter and an area. The bases of the trapezoid are two sides of the form that are parallel to one other. The non-parallel sides of a trapezoid are lateral sides. The altitude is the smallest distance between two parallel sides. If you are Calculating the area of a trapezoid is straightforward since the opposing sides are parallel to one other.

## Properties of Trapezoid

These are the following properties of a trapezoid that distinguish it from other quadrilaterals:

- The top and bottom bases are parallel to one another.
- A trapezoid’s opposite sides (isosceles) have the same length.
- The total angle of the angles that are close together is 180 degrees.
- The median is perpendicular to both bases.
- The length of the median is equal to the average of both bases, i.e. (a +b)/2.
- When both sets of opposing sides of a trapezoid are parallel, a parallelogram is created.
- A trapezoid may be called a square if both sets of opposing sides are parallel, all sides are equal length, and all sides are at right angles to each other.
- A trapezoid may be called a rectangle if both sets of opposing sides are parallel, opposite sides are of equal length, and opposite sides are at right angles to each other.

## Types of Trapezoids

Trapezoids are divided into three kinds

- Isosceles Trapezoid
- Scalene Trapezoid
- Right Trapezoid

## Isosceles Trapezoid

An isosceles trapezoid’s non-parallel sides have the same length. In the isosceles trapezoid, the angles of the parallel sides (base) are equal. A line of symmetry runs through an isosceles trapezoid, and both diagonals have the same length.

The trapezoid’s bases are XYZW, XY, and WZ in the isosceles trapezoid below. WX and YZ are known as the trapezoid’s legs since they are not parallel to each other.

## Scalene Trapezoid

A scalene trapezoid is one in which the sides and angles of the trapezoid are not equal. All four sides of the scalene trapezoid below, AB, BC, CD, and DA, are of different lengths. The bases, DC and AB, are parallel to one another but vary in length.

## Right Trapezoid

A right trapezoid is a trapezoid with two right angles, often known as a right-angled trapezoid. Trapezoids of this kind are used to determine the areas under the curve. The following right trapezoid or right-angled trapezoid has two right angles, one at D and the other at A. DC and AB are two opposing sides that are parallel to one another.

## Area of the Trapezoid

The area of a trapezoid can be noted by multiplying the average of the parallel sides by the height of the trapezoid. The lengths of two parallel sides of a trapezoid must be known, as well as the distance (height) between them, to calculate its area. It’s the number of unit squares that can fit within the form, and it’s expressed in square units like cm2, m2, in2, and so on. The area (A) of a trapezoid is determined using its bases, a and b, and its height, h, which is the perpendicular distance between them.

**Area of a trapezoid** is determined using the formula:

Area =[(AB + CD)/2] × h

A = [(a + b)/2] × h

Where,

AB and CD = parallel sides

a = shorter base

b = longer base

h = height or altitude

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