How do you use Heron's formula to determine the area of a triangle with sides of that are 25, 28, and 21 units in length?

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Answer 1 · 2015-12-29T08:36:04

#24sqrt111# #"units"^2#

Heron's formula:

#A=sqrt(s(s-a)(s-b)(s-c))#

When #s#, the semiperimeter, is equal to

#s=(a+b+c)/2#

when #a,b,c# are the sides of the triangle.

Find #s# first:

#s=(25+28+21)/2=37#

Thus,

#A=sqrt(37(37-25)(37-28)(37-21))#

#A=sqrt(37xx12xx9xx16)#

#A=sqrt37xxsqrt(2^2xx3)xxsqrt(3^2)xxsqrt(4^2)#

#A=(2xx3xx4)sqrt(37xx3)#

#A=24sqrt111~~252.8557#