SOLUTION: What is the area of triangle ABC if a=5ft, b=6ft, and c=7ft Can someone show me how to do it or explain it?

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Question 1116696: What is the area of triangle ABC if a=5ft, b=6ft, and c=7ft
Can someone show me how to do it or explain it?
Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
.
Use the Heron's formula for the area of a triangle:


    Area = sqrt%28s%28s-a%29%28s-b%29%28s-c%29%29 = ,


where  a,  b  and  c  are the measures of a triangle sides,   and  s  is the triangle semi-perimeter:  s = %28a+%2B+b+%2B+c%29%2F2. 


In your case the perimeter = 5 + 6 + 7 = 18ft;  sem-perimeter s = 18%2F2 = 9 ft,

and the formula works in this way 


    Area = sqrt%289%2A%289-5%29%2A%289-6%29%2A%289-7%29%29 = sqrt%289%2A4%2A3%2A2%29 = 3%2A2%2Asqrt%286%29 = 14.7 square ft.

On the Heron's formula see the lessons
    - Proof of the Heron's formula for the area of a triangle
    - One more proof of the Heron's formula for the area of a triangle
in this site.