document.write( "Question 877962: Find the area of a triangle whose sides are 9cm,10cm and 11cm \n" ); document.write( "

Algebra.Com's Answer #529630 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "\n" ); document.write( "

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.

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

$\"A=sqrt%28S%28S-a%29%28S-b%29%28S-c%29%29\"$ 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.

\n" ); document.write( " \n" ); document.write( "

\n" );