A triangle has sides with lengths: 16, 11, and 9. How do you find the area of the triangle using Heron's formula?

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Answer 1 · 2016-01-09T10:30:19

#sqrt2268 ≈ 47.62 #

Using Heron's formula is a two step process.

step 1 : find half of the triangles perimeter (s)

label the lengths of the 3 sides a , b and c.
In this case a = 16 , b = 11 and c = 9.

# s = ( a + b + c )/2 = ( 16 + 11 + 9 )/2 = 36/2 = 18 #

step 2 : Calculate the Area (A) using :

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

# rArr sqrt( 18(18 - 16 )(18 - 11 )(18 - 9 ) )= sqrt( 18 xx2 xx 7 xx 9) #

# rArr A = sqrt2268 ≈47.62 #