A triangle has sides with lengths: 7, 12, and 15. How do you find the area of the triangle using Heron's formula?

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Answer 1 · 2016-01-06T21:32:56

41.23 (2 decimal places )

this is a two step process

where a , b and c represent the three sides of the triangle

# color(red)( step 1 ) #

calculate s (half of the triangles perimeter ) : # s = (a + b + c)/2 #

in this case # s = (7 + 12 +15 )/2 = 34/2 = 17 #

# color(red)(step 2 ) #

calculate area : # A = sqrt( s(s - a )(s - b )(s - c )#

in this case A = # sqrt( 17(17 - 7 )(17 - 12 )(17 - 15 ) #

# rArr A = sqrt (17 xx 10 xx 5 xx 2 )= sqrt1700) = 41.23 #