While watching a movie, you must have had popcorn. Have you ever wondered what the shape of the popcorn bucket is? I am asking for a two-dimensional shape, not three dimensional one. Most of you may not be knowing this. It is of trapezoid shape. What is a trapezoid shape? How to find the area of that? Let us learn in detail about the properties of trapezoids.

A trapezoid is a two-dimensional shape with a pair of parallel sides and a pair of nonparallel sides. It belongs to the category of polygons. The pair of parallel sides are called bases of the trapezoid and the remaining nonparallel sides are called legs of the trapezoid.

## Properties of Trapezoid

Listed below are a few properties of a trapezoid:

- The top and bottom of the pyramid are parallel.
- Opposite sides of a trapezoid (isosceles) are of the same length.
- The angle between two adjacent angles sums up to 180°.
- The median runs parallel to both bases.
- Median’s length is the average of both the bases i.e. (a +b)/2.
- When the two pairs of the opposite sides are parallel in a trapezoid, it is considered a parallelogram.
- A trapezoid can be considered a square if the two pairs of opposite sides are parallel, all sides are equal in length, and all sides are at right angles to each other.
- 8. A trapezoid can be compared to a rectangle if the two pairs of its opposite sides are parallel, and its opposite sides have the same length.

## Area of a Trapezoid

To calculate the area of a trapezoid, the formula is:

Area of trapezoid = 1/2 (x + y) h

Where x is the length of the smaller base. Y is the length of the longer base and h is the altitude or the perpendicular distance between two bases.

The steps are:

- You can calculate the area of a trapezoid by taking the average of the two bases.
- Then this is multiplied by the altitude.
- Using this formula, you can calculate the area of a trapezoid.

## Perimeter of Trapezoid

Trapezoids have a perimeter equal to their sum of sides. In this case, the perimeter of a trapezoid with sides p, q, r, and s can be written as-

Perimeter of trapezoid = p + q + r + s

## Types of Trapezoids

There are three general types of trapezoids:

### 1. Right Trapezoids

Trapezoids with adjacent right angles are called right trapezoids. Under the trapezoidal rule, it is used to calculate the area under the curve.

### 2. Isosceles Trapezoids

It is called an isosceles trapezoid if the sides of the trapezoid that are not parallel are equal in length. Isosceles trapezoids have equal angles on their parallel sides (base). The diagonals of an isosceles trapezoid are equal in length and it has a line of symmetry.

### 3. Scalene Trapezoids

Trapezoids that have neither equal sides nor equal angles are called Scalene trapezoids.

## Worked Examples

Let us solve some problems on the area and perimeter of a trapezoid.

**Example 1: **Find the area of a trapezium having parallel sides of lengths 5 and 10 cm and the distance between them is 4 centimeters?

**Solution:** We have Area of trapezoid = 1/2 (x + y) h

Given x = 5cm, y = 10 cm and h = 4 cm

By substituting, we have

Area of trapezoid = 1/2 (5 + 10) 4

Area of trapezoid = 30cm2.

**Example 2:** The area of a trapezium is 400 square meters. The perpendicular distance between the bases is 16 meters and the length of one of its sides is 20 meters. Find the length of the other side?

**Solution:** We have Area of trapezoid = 1/2 (x + y) h

Given x = 20m, y = ?, h = 16 m and area = 400 m2.

By substituting, we have

Area of trapezoid = 1/2 (20 + y) 16 = 400

160 + 6y = 400

6y = 240

y = 40m.

For more solved problems and information log on to the Cuemath website.