Area of a Triangle

There are three common ways to compute the area of a triangle:

1. Basic formula that the area of a triangle is half the base times the height. This formula only works, of course, when you know what the height of the triangle is.

2. Heron's formula which gives the area in terms of the three sides of the triangle, specifically, as the square root of the product   s(s – a)(s – b)(s – c) , where s is the semiperimeter of the triangle, that is, s = (a + b + c)/2.

3. Sine/SAS (Side-Angle-Side) formula:

Area =1/2 ab SinC

That is to say, the area of a triangle is half the product of two sides times the sine of the included angle.