SOLUTION: What is the area of an isosceles triangle with sides of 7, 7, and 12?

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Question 475217: What is the area of an isosceles triangle with sides of 7, 7, and 12?

Found 2 solutions by jim_thompson5910, richard1234:
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=%287%2B7%2B12%29%2F2 Plug in a=7, b=7, and c=12.



S=%2826%29%2F2 Add.



S=13 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%2813%2813-7%29%2813-7%29%2813-12%29%29 Plug in S=13, a=7, b=7, and c=12.



A=sqrt%2813%286%29%286%29%281%29%29 Subtract.



A=sqrt%28468%29 Multiply.



A=21.6333076527839 Take the square root of 468 to get 21.6333076527839.



So the area of the triangle with side lengths of a=7, b=7, and c=12 is roughly 21.6333076527839 square units.




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Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
You can use Heron's formula. Or, given that the triangle is isosceles you can draw an altitude from the vertex to the base (of length 12) so that you have two right triangles with legs h and 6, and hypotenuse 7. Here it should be pretty easy.