Course: Trigonometry
Topic: Oblique Triangles and the Laws
Subtopic: Area of a Triangle


Remember the area of a triangle formula `A=1/2bh`? This formula works on both right and oblique triangles, but you have to know the length of the altitude (h) of the triangle. In the triangles we have been working with lately, we aren't given the altitude, just sides and/or angles. So, new area formulas would be useful.

The common `A=1/2bh` formula is actually a special case of the area of a triangle formula `A=1/2ab*sin gamma` where gamma is the included angle between sides of length a and b. This formula can be used to find the area of an oblique triangle given SAS.

To find the area of an oblique triangle given SSS, use Heron's Area Formula, `A=sqrt(s(s-a)(s-b)(s-c))` where s is the semiperimeter of the triangle. This formula has an interesting history and extends into higher dimensions. See the supplementary resources below for more information.


By the end of this topic you should know and be prepared to be tested on:


Terms you should be able to define: semiperimeter `s=1/2(a+b+c)`
Heron's Area Formula `A=sqrt(s(s-a)(s-b)(s-c))`
Area formula `A=1/2ab*sin gamma`

Mini-Lectures and Examples

STUDY: Oblique Triangles - Law of Cosines & Area of a Triangle

Supplementary Resources

rev. 2020-11-09