Chapter 8.4, Problem 3AYU

The area $K$ of a triangle with sides $a$, $b$, and $c$ is $K=\_\_\_\_\_\_\_$, where $s=\_\_\_\_\_\_\_$.

To determine

To fill: The area $\text{K}$ of a triangle with sides $\text{a}$, $\text{b}$, and $\text{c}$ is $\text{K}$ = ________, where $\text{s}$ = ________.

Answer to Problem 3AYU

Solution:

$K = \sqrt{s \left(s - a\right) \left(s - b\right) \left(s - c\right)}$, $\text{s} = (\text{a} + \text{b} + \text{c})$

Explanation of Solution

Given:

The area $\text{K}$ of a triangle with sides $\text{a}$, $\text{b}$, and $\text{c}$ is

$\text{K}$ = ________, where $\text{s}$ = ________.

Calculation:

If the three sides of a triangle are known, formula, called Heron’s Formula (named after Heron of Alexandria), can be used to find the area of a triangle.

Heron’s Formula

The area $\text{K}$ of a triangle with sides $\text{a}$, $\text{b}$, and $\text{c}$ is

$K = \sqrt{s \left(s - a\right) \left(s - b\right) \left(s - c\right)}$

where $\text{s} = (\text{a} + \text{b} + \text{c})$