Question

How do you use Heron's formula to determine the area of a triangle with sides of that are 6, 4, and 8 units in length?

Answer 1

≈ 11.62 square units

Explanation:

This is a 2 step process.

Step 1: calculate half the sum (s ) of the perimeter

`color(red)(|bar(ul(color(white)(a/a)color(black)(s=(a+b+c)/2)color(white)(a/a)|)))`

let a = 6 , b = 4 and c = 8 ( the sides of the triangle)

`rArrs=(6+4+8)/2=18/2=9`

Step 2: calculate the area (A ) using

`color(red)(|bar(ul(color(white)(a/a)color(black)(A=sqrt(s(s-a)(s-b)(s-c)))color(white)(a/a)|)))`

`A=sqrt(9(9-6)(9-4)(9-8))`

`=sqrt(9xx3xx5xx1)=sqrt135≈11.62 (2 "decimal places")`