SOLUTION: formula for solving area of triangle of 5cm 6cm 7cm

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Question 765579: formula for solving area of triangle of 5cm 6cm 7cm
Answer by jim_thompson5910(35256) About Me  (Show Source):
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Solved by pluggable solver: Hero's (or Heron's) Formula (Used to Find the Area of a Triangle Given its Three Sides)


In order to find the area of a triangle 'A' with side lengths of 'a', 'b', and 'c', we can use Hero's Formula:



A=sqrt%28S%28S-a%29%28S-b%29%28S-c%29%29 where S is the semiperimeter and it is defined by S=%28a%2Bb%2Bc%29%2F2

Note: "semi" means half. So the semiperimeter is half the perimeter.



So let's first calculate the semiperimeter S:



S=%28a%2Bb%2Bc%29%2F2 Start with the semiperimeter formula.



S=%285%2B6%2B7%29%2F2 Plug in a=5, b=6, and c=7.



S=%2818%29%2F2 Add.



S=9 Divide.



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A=sqrt%28S%28S-a%29%28S-b%29%28S-c%29%29 Now move onto Hero's Formula.



A=sqrt%289%289-5%29%289-6%29%289-7%29%29 Plug in S=9, a=5, b=6, and c=7.



A=sqrt%289%284%29%283%29%282%29%29 Subtract.



A=sqrt%28216%29 Multiply.



A=14.6969384566991 Take the square root of 216 to get 14.6969384566991.



So the area of the triangle with side lengths of a=5, b=6, and c=7 is roughly 14.6969384566991 square units.