Modules · Module 06

Area of a triangular system

Area is half the product of two sides and the sine of the included angle. Several equivalent formulas exist so you can start from whatever is given.

Area = (1/2) ab sin C s = (a+b+c)/2 Area = √[s(s−a)(s−b)(s−c)]

Base and height

Area = (1/2) × base × corresponding height. Any side may serve as the base.

Area = (1/2) ab sin C. This is the SAS area formula and works for acute or obtuse C, because sine is positive in both quadrants used here.

From three sides: let s be the semi-perimeter. Then Area = √[s(s−a)(s−b)(s−c)].

Useful when no angle is known and you do not want to compute one first.