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?

2 Answers
Sihan Tawsik
Feb 4, 2016

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#

Jim G.
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 = (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 #

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