Trapezoid
(Jump to Area of a Trapezoid or Perimeter of a Trapezoid)
A trapezoid is a 4sided 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 Isosceles trapezoid when both angles coming from a parallel side are equal, and the sides that aren't parallel are equal in length. 

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 average of the two base lengths times the altitude: 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 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
The median (also called a midline or midsegment) is a line segment halfway between the two bases. 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 