document.write( "Question 877138: An artist needs to know the area of a triangular piece of stained glass with sides measuring 9 cm, 7 cm, and 5 cm. What is the area to the nearest square centimeter? \n" ); document.write( "

Algebra.Com's Answer #529186 by jim_thompson5910(35256) $\"\"$ $\"About$

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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.

$\"S=%289%2B7%2B5%29%2F2\"$ Plug in $\"a=9\"$ , $\"b=7\"$ , and $\"c=5\"$ .

$\"S=%2821%29%2F2\"$ Add.

$\"S=10.5\"$ Divide.

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

$\"A=sqrt%2810.5%2810.5-9%29%2810.5-7%29%2810.5-5%29%29\"$ Plug in $\"S=10.5\"$ , $\"a=9\"$ , $\"b=7\"$ , and $\"c=5\"$ .

$\"A=sqrt%2810.5%281.5%29%283.5%29%285.5%29%29\"$ Subtract.

$\"A=sqrt%28303.1875%29\"$ Multiply.

$\"A=17.4122801493658\"$ Take the square root of $\"303.1875\"$ to get $\"17.4122801493658\"$ .

So the area of the triangle with side lengths of $\"a=9\"$ , $\"b=7\"$ , and $\"c=5\"$ is roughly $\"17.4122801493658\"$ square units.

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