# Area of a trapezium

## Prerequisites

### Area of a trapezium

#### Introduction

• A trapezium is a 4 sided shape in which one pair of opposite sides is parallel:
• The parallel sides are called the bases: b1 and b2.
• The distance between the bases is called the height: h.
• The equation for the area of a trapezium is:

#### Proof

• If we duplicate the trapezium and rotate it:
• Then we see that the two trapeziums together form a parallelogram.
• The area of a parallelogram is:
• Which in our case is:
• And we just divide this by two (as we only want the area of one of the trapeziums):

#### Code (Python)

base1, base2 = 4, 2
height = 3

area = (base1 + base2) * height / 2
print(area) # prints 9.0