SOLUTION: the length of the sides of a triangle are 6 inches, 8 inches, and 12 inches. Find the area of the triangle

Algebra ->  Triangles -> SOLUTION: the length of the sides of a triangle are 6 inches, 8 inches, and 12 inches. Find the area of the triangle      Log On


   

Question 602476: the length of the sides of a triangle are 6 inches, 8 inches, and 12 inches. Find the area of the triangle
Found 2 solutions by ewatrrr, jim_thompson5910:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,



Using Heron's Equation to find the area of a triangle when 3 sides are given

a = 6, b = 8 and c  = 12 inches 

sqrt%28s%28s-a%29%28s-b%29%28s-c%29%29  | s being the semi-perimeter = 26/2 = 13

sqrt%2813%287%29%285%29%281%29%29 = 21.3307 square inches

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=%286%2B8%2B12%29%2F2 Plug in a=6, b=8, and c=12.



S=%2826%29%2F2 Add.



S=13 Divide.



----------------------------------------



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



A=sqrt%2813%2813-6%29%2813-8%29%2813-12%29%29 Plug in S=13, a=6, b=8, and c=12.



A=sqrt%2813%287%29%285%29%281%29%29 Subtract.



A=sqrt%28455%29 Multiply.



A=21.3307290077015 Take the square root of 455 to get 21.3307290077015.



So the area of the triangle with side lengths of a=6, b=8, and c=12 is roughly 21.3307290077015 square units.