How do you derive the formula for a triangle?

1 Answer
Dec 26, 2015

Probably, the question is about a formula for an area of a triangle.
If not, ask more specifically.
Below is the proof of a formula #S=1/2*a*h#,
where #a# is a base and #h# is an altitude.

Explanation:

Consider triangle #Delta ABC# below
enter image source here

An altitude #h# separates our triangle into two right triangles.
As seen from the picture, the area of each one of these right triangles is doubled, so the area of a rectangle with the same base #a# and altitude #h# is twice the area of an initial triangle.

Since the area of a rectangle is #a*h#, the area of the initial triangle is
#S = 1/2*a*h#

The drawing will be different in case of a triangle with an obtuse angle at the base. In this case an analogous transformation into a rectangle will represent our triangle not as a sum of two right triangles, but as their difference with the same final formula.