Chapter 8.4, Problem 10AYU

To determine

To find: The area of the given triangle.

Answer to Problem 10AYU

Solution:

$Area \approx 8.18$

Explanation of Solution

Given:

Formula used:

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

Calculation:

$a = 8, b = 5, c = 4$

Area of the triangle is given by

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

Where $s = \frac{a + b + c}{2}$

$s = \frac{8 + 5 + 4}{2} = \frac{17}{2}$

$K = \sqrt{( \frac{17}{2}) \left(\frac{17}{2} - 8\right) \left(\frac{17}{2} - 5\right) \left(\frac{17}{2} - 4\right)}$

$K = \frac{3\sqrt{119}}{4}$

$K \approx 8.18$

$Area \approx 8.18$