How do you use Heron's formula to find the area of a triangle with sides of lengths #14 #, #8 #, and #11 #?

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Answer 1 · 2016-04-19T15:06:13

Area of triangle is #87.83#

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 #14#, #8# and #11#, #s=1/2(14+8+11)=33/2# and hence area of the triangle is

#sqrt(33/2xx(33/2-14)xx(33/2-8)xx(33/2-11))#

= #sqrt(33/2xx5/2xx17/2xx11/2)#

= #1/2sqrt(11xx3xx5xx17xx11)=11/2sqrt(15xx17)#

= #11/2sqrt255=11/2xx15.969=87.83#