# Trapezoid: Definition, Kinds, Area & Perimeter Formula, Examples

Geometry is one of mathematics’ branch. It has many shapes that one of them is plane geometry. In plane geometry, there is quadrilateral shape that has many kinds of it. One of them is trapezoid.

In daily life, trapezoid can be found in handbag, bridges, and popcorn box in cinema.

## Definition of Trapezoid

Trapezoid is one of special shapes of plane geometry. In definition, trapezoid is quadrilateral (four-sides shape) that has a pair of parallel sides in opposite. Besides that, the total angles in next to each other is 180°.

In general, trapezoid has bases in top and bottom (a and b), height (h), and sloping side (legs).

Trapezoid has different name between US and British. The differences are:

## Kinds of trapezoid

There are some kinds of trapezoids.

### 1. Right Trapezoid

Right trapezoid has a pair of parallel line and two right angles.

### 2. Isosceles Trapezoid

Isosceles trapezoid has same angles on the base. Consequently, the sloping sides (legs) are same length.

### 3. Scalene Trapezoid

Scalene trapezoid is one of kind of trapezoid that has not equal sides and equal angles.

## Area of a Trapezoid

Area of trapezoid use the parallel sides and altitude (height)

Area = A = [(a+b)/2] x h

## Perimeter of a Trapezoid

Perimeter means length of all sides. In another words, perimeter of trapezoids is sum of all of the lengths.

Perimeter = P = a + b + c + d

## Median of a Trapezoid

Median means middle part of something. Median of a trapezoid means a line that separate it to be two parts and each of them has a half of the height. It is parallel with the bases (top and bottom).

The length of median is average of the parallel line.

Median = (a+b)/2

## Examples

1. Determine which statement(s) is(are) true.

a. Trapezoid is a rectangle
b. Trapezoid always has a right angle.
c. Trapezoid always has four sides.
d. Isosceles trapezoid has same length of sloping sides.

Example

a. Trapezoid is a rectangle (false, because rectangle is special shape of trapezoid)

b. Trapezoid always has a right angle. (false, there is only right trapezoid that has right angles)

c. Trapezoid always has four sides (true because trapezoid is one of quadrilateral shape).

d. Isosceles trapezoid has same length of sloping sides (true because it has same angles in base therefore it has same length in sloping sides)

2. Determine ratio of the area and perimeter of the trapezoid.

Example

First step is completing the length of each sides.

a = 6 cm

h = 4 cm

b = 6 + 3 + 3 = 12 cm

sloping side (using Pythagoras) = 5 cm

then

• area = [(a+b)/2] x h

= [(6 + 12)/2] x 4

= 9 x 4

= 36 cm2

• perimeter = a + 2 sloping sides + b

= 6 + (2 x 5) + 12

= 6 + 10 + 12

= 28 cm

• ratio of area and perimeter

area : perimeter = 36 : 28

= 9 : 7

3. Determine the value of x.

Example

Focus on triangle, let base is y.

Using Pythagorean theorem,

y = √(152 – 122)

= √(225 – 144)

= √81

= 9

Then x = 24 – 9 = 15 cm