Question

How do you use Heron's formula to determine the area of a triangle with sides of that are 12, 18, and 19 units in length?

Answer 1

≈104.635 square units

Explanation:

This is a 2 step process.

Step 1: Calculate half of the perimeter (s ) of the triangle

`color(red)(|bar(ul(color(white)(a/a)color(black)(s=(a+b+c)/2)color(white)(a/a)|)))`
where a , b and c are the sides of the triangle

let a = 12 , b = 18 and c = 19

`rArrs=(12+18+19)/2=49/2=24.5`

Step 2: Calculate the area (A ) using

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

`=sqrt(24.5(24.5-12)(24.5-18)(24.5-19))`

`=sqrt(24.5xx12.5xx6.5xx5.5)≈104.635" square units"`