How do you use Heron's formula to determine the area of a triangle with sides of that are 14, 16, and 17 units in length?

Question

1364 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-04-10T17:44:05

#=104.324# square units

Heron's formula for area of triangle is:

#A = sqrt(s(s-a)(s-b)(s-c)#, where #s# is the semi-pertimeter.

#=>s=(a+b+c)/2#

Here, #a=14#, #b=16# and #c=17#.

First find #s#:

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

#=(14+16+17)/2=47/2#

Now to calculate the area:

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

#= sqrt(47/2(47/2-14)(47/2-16)(47/2-17)#

#= sqrt(47/2((47-28)/2)((47-32)/2)((47-34)/2)#

#= sqrt(47/2(19/2)(15/2)(13/2)#

#=sqrt((47xx19xx15xx13)/16)#

#=1/4sqrt(47xx19xx15xx13)#

#=1/4sqrt(174135)#

#=1/4xx417.294#

#=104.324#