SOLUTION: Find the area of a triangle whose sides are 9cm,10cm and 11cm

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Question 877962: Find the area of a triangle whose sides are 9cm,10cm and 11cm
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
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=%289%2B10%2B11%29%2F2 Plug in a=9, b=10, and c=11.



S=%2830%29%2F2 Add.



S=15 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%2815%2815-9%29%2815-10%29%2815-11%29%29 Plug in S=15, a=9, b=10, and c=11.



A=sqrt%2815%286%29%285%29%284%29%29 Subtract.



A=sqrt%281800%29 Multiply.



A=42.4264068711929 Take the square root of 1800 to get 42.4264068711929.



So the area of the triangle with side lengths of a=9, b=10, and c=11 is roughly 42.4264068711929 square units.