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

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Question 475218: What is the area of an isosceles triangle with sides of 7, 7, and 12
Found 2 solutions by jim_thompson5910, robertb:
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 robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Since it is an isosceles triangle, we can find its height by using half of the base side and the Pythagorean Theorem:
h+=+sqrt%287%5E2+-+%2812%2F2%29%5E2%29+=+sqrt%2849+-+36%29+=+sqrt%2813%29
==> Area = A+=+%281%2F2%29%2Abh+=+%281%2F2%29%2A12%2Asqrt%2813%29+=+6sqrt%2813%29.