How do you use Heron's formula to determine the area of a triangle with sides of that are 15, 16, and 12 units in length?

1 Answer
Shwetank Mauria
Apr 11, 2016

Area of triangle is #107.32# units.

Explanation:

If three sides of a triangle are #a#, #b# and #c#, according to Heron's formula its area is given by

#sqrt(s(s-a)(s-b)(s-c))#, where #s=1/2(a+b+c)# is semi perimeer of the triangle.

In the given triangle the three sides are #15#, #16# and #12# and semi perimeter is #1/2xx(15+16+12)=1/2xx43=21.5#.

Hence area is given by

#sqrt(22.5(22.5-15)(22.5-16)(22.5-12))#

or #sqrt(22.5xx7.5xx6.5xx10.5)=sqrt11517.1875=107.32#

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