How do you use Heron's formula to determine the area of a triangle with sides of that are 8, 5, and 10 units in length?

Feb 4, 2016

here is how,

Explanation:

we know,

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

$= \frac{8 + 10 + 5}{2}$

$= \frac{23}{2}$

$= 11.5$

from heron's formula, we know,

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

$= \sqrt{11.5 \left(11.5 - 8\right) \left(11.5 - 5\right) \left(11.5 - 10\right)}$

$= \sqrt{392.4375}$

$= 19.8100353357 u n i {t}^{2}$

Feb 4, 2016

Area ≈ 19.8

Explanation:

This is a 2 step process :

1. Calculate half of the triangle's perimeter (s)

2. Calculate the area

let a = 8 , b = 5 and c = 10

step 1 : $s = \frac{a + b + c}{2} = \frac{8 + 5 + 10}{2} = \frac{23}{2} = 11.5$

step 2 : Area $= \sqrt{s \left(s - a\right) \left(s - b\right) \left(s - c\right)}$

 = sqrt(11.5(11.5-8)(11,5-5(11.5-10)

= sqrt(11.5 xx 3.5 xx 6.5 xx 1.5) ≈ 19.8