# How do you use Heron's formula to determine the area of a triangle with sides of that are 14, 8, and 17 units in length?

Jun 3, 2018

color(indigo)(A_t = 55.53 sq units

#### Explanation:

$a = 14 , b = 8 , c = 17$

According to Heron’s formula, area of triangle

${A}_{t} = \sqrt{s \left(s - a\right) \left(s - b\right) \left(s - c\right)}$ where s is the semi perimeter & $= \frac{a + b + c}{2}$

$s = \frac{14 + 8 + 17}{2} = 19.5$

${A}_{t} = \sqrt{19.5 \cdot \left(19.5 - 14\right) \left(19.5 - 8\right) \left(19.5 - 17\right)}$

color(indigo)(A_t = 55.53 sq units