Question

How do you use Heron's formula to determine the area of a triangle with sides of that are 6, 5, and 8 units in length?

Answer 1

≈ 14.98 square units

Explanation:

This is a 2 step process.

Step 1
Calculate half 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)|)))`

let a = 6 , b = 5 and c = 8

`rArr s = (6+5+8)/2 = 19/2 = 9.5`

Step 2

Calculate the area (A) using

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

`rArr A = sqrt(9.5(9.5-6)(9.5-5)(9.5-8))`

`= sqrt(9.5xx3.5xx4.5xx1.5) ≈ 14.98" square units "`