How do you use Heron's formula to find the area of a triangle with sides of lengths #3 #, #7 #, and #7 #?

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Answer 1 · 2016-02-28T03:18:36

The area is #~~10.3# square units

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

The semi-perimeter is half the perimeter, with the formula #s=(a+b+c)/2#.

Let
#a=3#
#b=7#
#c=7#

Solution
Determine semi-perimeter, then substitute known values into Heron's formula and solve.

#s=(3+7+7)/2#

#s=17/2#

#s=8.5#

#A=sqrt(8.5(8.5-3)(8.5-7)(8.5-7))#

#A=sqrt(8.5(5.5)(1.5)(1.5))#

#A=sqrt(101.1875)#

#A=10.3# square units rounded to one decimal place