The area of a triangle is
where
is the base and
is the perpendicular height. This formula is a bit artififical because we can take any side as the base and the height will be the perendicular distance of the opposite vertex from this chosen base.
There is another very useful formula,
whereand
are two sides and
is the angle between them. This formula can be derived from the triangle above.
Make a right angled triangle as below and label the anglesand
and the side
Using simple trigonometry for the right angled triangle gives
Use the identity
so
and
Then