Question

A triangle has sides with lengths: 4, 5, and 4. How do you find the area of the triangle using Heron's formula?

Answer 1

area ≈ 7.806 square units

Explanation:

This is a 2 step process.

Step 1

Calculate half the perimeter (s) of the triangle

let a = 4 , b = 5 and c = 4

`s=(a+b+c)/2=(4+5+4)/2=13/2=6.5`

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(6.5(6.5-4)(6.5-5)(6.5-4))`

`=sqrt(6.5xx2.5xx1.5xx2.5) ≈ 7.806" square units"`