Question

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

Answer 1

`~~6.437" to 3 dec. places"`

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`