A triangle has sides with lengths: 14, 15, and 7. How do you find the area of the triangle using Heron's formula?

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Answer 1 · 2016-04-02T07:34:44

$2sqrt594$

Use Heron's formula

$color(blue)(area=sqrt(s(s-a)(s-b)(s-c))$

Where

$color(orange)((a,bandc)=sides,s=(a+b+c)/2$

So,

$color(purple)(a=14,b=15,c=7,s=(14+15+7)/(2)=36/2=18$

$:.area=sqrt(18(18-14)(18-15)(18-7))$

$rarrsqrt(18(4)(3)(11))$

$rarrsqrt(18(132))$

$rarrsqrt2376$

$rarrsqrt(4*594)$

$color(green)(rArr2sqrt594~~48.7bar5$