How do you use Heron's formula to find the area of a triangle with sides of lengths #4 #, #5 #, and #7 #?

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Answer 1 · 2016-04-19T09:15:04

Area of the triangle is #7.483#

According to Heron's formula, area of a triangle whose three sides are #a#, #b# and #c# is given by #sqrt(s(s-a)(s-b)(s-c))#, where #s=1/2(a+b+c)#.

As in given case three sides are #4#, #5# and #7#, #s=1/2(4+5+7)=16/2=8# and hence area of the triangle is

#sqrt(8xx(8-4)xx(8-5)xx(8-7))=sqrt(8xx4xx3xx1)=sqrt56=7.483#