# How do you use Heron's formula to determine the area of a triangle with sides of that are 12, 5, and 8 units in length?

Feb 28, 2016

$\approx 14.52 . s q . u n i t s$

#### Explanation:

Use Heron's formula

color(brown)(sqrt(s(s-a)(s-b)(s-c))

Where

color(blue)(a-b-c=sides,s=(a+b+c)/2

In this case

color(blue)(a=12,b=5,c=8,s=(12+5+8)/2=25/2=12.5

So

$A r e a = \sqrt{12.5 \left(12.5 - 12\right) \left(12.5 - 5\right) \left(12.5 - 8\right)}$

=sqrt(12.5(0.5)(7.5)(4.5)

color(green)(=sqrt(210.9375)~~14.52.sq.units