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S = contains supplemental resources
Course: Trigonometry
Topic: Oblique Triangles and the Laws
Subtopic: Area of a Triangle

Overview

Remember the area of a triangle formula A=½bh? 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=½bh formula is actually a special case of the area of a triangle formula A=½ab·sinγ 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=√[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.

Objectives

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

• 7.4.1 Find the area of an oblique triangle given SSS via Heron's Area Formula
• 7.4.2 Find the area of an oblique triangle given SAS

Terminology

Define: semiperimeter s=(a+b+c)/2,
Heron's Area Formula A=√[s(s-a)(s-b)(s-c)],
Area formula A=½ab·sinγ

Supplementary Resources