How do you use Heron's formula to determine the area of a triangle with sides of that are 9, 15, and 10 units in length?

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Answer 1 · 2016-01-11T08:02:21

#Area=43.6348# square units

Hero's formula for finding area of the triangle is given by
#Area=sqrt(s(s-a)(s-b)(s-c))#

Where #s# is the semi perimeter and is defined as
#s=(a+b+c)/2#

and #a, b, c# are the lengths of the three sides of the triangle.

Here let #a=9, b=15# and #c=10#

#implies s=(9+15+10)/2=34/2=17#

#implies s=17#

#implies s-a=17-9=8, s-b=2 and s-c=7#

#implies s-a=8, s-b=2 and s-c=7#

#implies Area=sqrt(17*8*2*7)=sqrt1904=43.6348# square units

#implies Area=43.6348# square units