Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 7 - Applications of Trigonometric Functions - Section 7.4 Area of a Triangle - 7.4 Assess Your Understanding - Page 567: 56


$K=\sqrt{s(s-a)(s-b)(s-c)}$, where $s=\dfrac{a+b+c}{2}$

Work Step by Step

According to Heron's formula, the area of a triangle with sides $a,b$ and $c$ is given by: $K=\sqrt{s(s-a)(s-b)(s-c)}$ where $s=\dfrac{a+b+c}{2}$ and $K$ is the area of the triangle. Therefore, the area of a triangle when the lengths of the three sides are known can be calculated with the above formula.
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