# How do you use Heron's formula to find the area of a triangle with sides of lengths #7 #, #5 #, and #6 #?

##### 1 Answer

Jan 30, 2016

#A = sqrt(s(s-a)(s-b)(s-c)) = 6sqrt(6) ~~ 14.6969#

#### Explanation:

Heron's formula tells us that the area

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

Where *semi-perimeter*

In our case, let

Then

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

#=sqrt(9 * (9-7) * (9-5) * (9-6))#

#=sqrt(9*2*4*3)#

#= sqrt(36*6) = sqrt(36)*sqrt(6) = 6sqrt(6) ~~ 14.6969#