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.

Trapezoid (or Trapezium)
Trapezoid
Isosceles Trapezoid
A pair of parallel sides

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

Called a "Trapezium" in the UK

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 average of the two base lengths times the altitude:

Area =  a+b  × h
2

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

Area = (6 m + 4 m)/2 × 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.

 

The Perimeter is the sum of all side lengths:

Perimeter = a+b+c+d

Example: A trapezoid has side length 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 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+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