A triangle has sides with lengths: 14, 9, and 12. How do you find the area of the triangle using Heron's formula?

1 Answer
Meave60
Jan 7, 2016

The area of the triangle is 53.5 square units.

Explanation:

Heron's formula is #A=sqrt(s(s-a)(s-b)(s-c))#, where #A# is area, #a, b,# and #c# are the sides of the triangle, and #s# is the semiperimeter, which is half the perimeter.

The formula for the semiperimeter is #s=(a+b+c)/2#.

Let side #a=14#, side #b=9#, and side #c=12#.

Calculate the semiperimeter.

#s=(14+9+12)/2#

#s=35/2=17.5#

Calculate the area of the triangle.

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

#A=sqrt((17.5)(17.5-14)(17.5-9)(17.5-12))#

#A=53.5# square units

Source: https://www.mathsisfun.com/geometry/herons-formula.html

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