Question

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?

Answer 1

here is how,

Explanation:

we know,

`s=(a+b+c)/2`

`=(8+10+5)/2`

`=23/2`

`=11.5`

from heron's formula, we know,

`A=sqrt(s(s-a)(s-b)(s-c))`

`=sqrt(11.5(11.5-8)(11.5-5)(11.5-10))`

`=sqrt(392.4375)`

`=19.8100353357unit^2`

Answer 2

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 = (a+b+c)/2 = (8+5+10)/2 = 23/2 = 11.5`

step 2 : Area `= sqrt(s(s-a)(s-b)(s-c) )`

`= 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`