Question

How do you use Heron's formula to determine the area of a triangle with sides of that are 25, 28, and 27 units in length?

Answer 1

≈ 305.94 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)|)))`
where a ,b and c are the sides of the triangle.

let a = 25 , b =28 and c = 27

`rArrs=(25+28+27)/2=80/2=40`

Step 2 Calculate the area (A ) using the formula.

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

`rArrA=sqrt(40(40-25)(40-28)(40-27))`

`=sqrt(40xx15xx12xx13)≈305.94" square units"`