# A triangle has sides with lengths: 7, 2, and 8. How do you find the area of the triangle using Heron's formula?

##### 1 Answer

Mar 26, 2018

#### Explanation:

#"Heron's formula is in 2 parts"#

#• " calculate the semi-perimeter (s)"#

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

#"where a, b and c are the sides of the triangle"#

#"let "a=7, b=2" and "c=8#

#rArrs=(7+2+8)/2=17/2#

#• " calculate the area (A) using the formula"#

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

#color(white)(A)=sqrt(17/2(17/2-7)(17/2-2)(17/2-8))#

#color(white)(A)=sqrt(17/2(3/2)(13/2)(1/2))#

#color(white)(A)=sqrt(663/16)~~6.437#