Question

A triangle has sides with lengths: 4, 5, and 7. How do you find the area of the triangle using Heron's formula?

Answer 1

`4sqrt6 ≈ 9.8 " square units "`

Explanation:

This is a 2 step process.

step 1 : Calculate half of the perimeter ( s ) of the triangle.
step 2 : Calculate the area (A)

let a = 4 , b = 5 and c = 7

step 1 : s = `(a + b + c )/2 = (4 + 5 + 7)/2 = 16/2 = 8`

step 2 : `A = sqrt(s(s-a)(s-b)(s-c) )`

`= sqrt(8(8-4)(8-5)(8-7)) = sqrt(8 xx 4 xx 3 xx 1) =sqrt96 = 4sqrt6`

Answer 2

`Area=4sqrt6.units`

Explanation:

`A=Area`

`a-b-c=sides`

`s=(a+b+c)/2`

Heron's formula for the area of the triangle:

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

In this case `color(green)(a=4,b=5,c=7,s=(4+5+7)/2=16/2=8`

`rarrA=sqrt(8(8-4)(8-5)(8-7))`

`rarrA=sqrt(8(4)(3)(1))`

`rarrA=sqrt(8(12))`

`rArrcolor(orange)(A=sqrt96=sqrt(16*6)=4sqrt6`