Proof of Formula for the Area of a Triangle

A triangle doesn't need to be right – angled for the area to be easily found. For the triangle – not rightangled, equliateral or isosceles - labelled as below,

The area is calculated from

To prove this formula, draw a line from B to meet the line AC (the side labelled b) at right angles.

The side b can then be used as the base of the triangle and BO is the height.

For the triangle ABO,so thatand the area of the triangle is

We can think of the formula as

Using this alternative definition we can also write