How do you use Heron's formula to determine the area of a triangle with sides of that are 12, 5, and 8 units in length?

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Answer 1 · 2016-02-28T13:39:25

$~~14.52.sq.units$

Use Heron's formula

$color(brown)(sqrt(s(s-a)(s-b)(s-c))$

Where

$color(blue)(a-b-c=sides,s=(a+b+c)/2$

In this case

$color(blue)(a=12,b=5,c=8,s=(12+5+8)/2=25/2=12.5$

So

$Area=sqrt(12.5(12.5-12)(12.5-5)(12.5-8))$

$=sqrt(12.5(0.5)(7.5)(4.5)$

$color(green)(=sqrt(210.9375)~~14.52.sq.units$