In my previous blog titled “An Algebraic Proof of Heron’s Formula“, I algebraically derived the Heron’s formula concerning *A*, the area of a triangle:

where a, b, c are three sides of a triangle and .

There is an alternative derivation which requires some basic trigonometry.

Here it is:

Fig. 1

Let (see Fig. 1), then

i.e.,

due to trigonometric identity .

Moreover, by the law of cosines, which implies

,

and (1) becomes

Hence,

.

MomHi son !

Keep up the good work!

Love,

Mom