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
Trapezoid   Isosceles Trapezoid

A trapezoid:

right arrow has a pair of parallel sides
right arrow

is an Isosceles trapezoid when both angles coming from a parallel side are equal, and the sides that aren't parallel are equal in length.

right arrow is called a "Trapezium" in the UK (see below)

Play with a trapezoid:

 

trapezoid base leg and altitude

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

trapezoid a, b, h  

The Area is the average of the two base lengths times the altitude:

Area = a+b2 × h

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

Area  =  6 m + 4 m2 × 3 m  =  5 m × 3 m  =  15 m2

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.

trapezoid perimeter a+b+c+d  

The Perimeter is the sum of all side lengths:

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

trapezoid median half-way between a and b  

The median (also called a midline or midsegment) is a line segment half-way between the two bases.

The median's length is the average of the two base lengths:

m = a+b2

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