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

2 Answers
Jim G.
Feb 17, 2016

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

Veddesh phi
Feb 17, 2016

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

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