# Trapezoid

*(Jump to Area of a Trapezoid or Perimeter of a Trapezoid) *

A trapezoid is a 4-sided flat shape with straight sides that has **a pair of opposite sides parallel** (marked with arrows below):

Trapezoid | Isosceles Trapezoid |

A trapezoid:

has a pair of parallel sides | |

is an | |

is called a "trapezium" in the UK (see below) |

Play with a trapezoid:

The parallel sides are the "bases"

The other two sides are the "legs"

The distance (at right angles) from one base to the other is called the "altitude"

## Area of a Trapezoid

The Area is the Area = \frac{a+b}{2} × h |

### Example: A trapezoid's two bases are 6 m and 4m, and it is 3m high. What is its Area?

Area = \frac{6 m + 4 m}{2} × 3 m = 5 m × 3 m = **15 m ^{2}**

The Area of Polygon by Drawing tool is helpful when you can draw your Trapezoid.

## Perimeter of a Trapezoid

The Perimeter is the distance around the edges.

The Perimeter is Perimeter = a+b+c+d |

### Example: A trapezoid has side lengths of 5 cm, 12 cm, 4 cm and 15 cm, what is its Perimeter?

Perimeter = 5 cm + 12 cm + 4 cm + 15 cm = **36 cm**

## Median of a Trapezoid

The The median's length is the average of the two base lengths: m = \frac{a+b}{2} |

You can calculate the area when you know the median, it is just the median times the height:

Area = mh

## Trapezium

A **trapezium** (UK: trapezoid) is a quadrilateral with NO parallel sides.

The US and UK have their definitions swapped over, like this:

Trapezoid | Trapezium | |

US: | a pair of parallel sides | NO parallel sides |

UK: | NO parallel sides | a pair of parallel sides |