Monday, June 16, 2008

`a = 3/5, b = 5/8, c = 3/8` Use Heron's Area Formula to find the area of the triangle.

The Heron's Formula is used to compute the area of the triangle when the three sides are known. The formula is:


`A = sqrt(s(s-a)(s-b)(s-c))`


where s is the semi-perimeter of the triangle, and a, b and c are the length of the sides.


The semi-perimeter of the given triangle is:


`s=(a+b+c)/2=(3/5+5/8+3/8)/2=(8/5)/2=4/5`


Plugging the values of s, a, b and c to the formula of area of triangle yields:


`A=sqrt(s(s-a)(s-b)(s-c))=sqrt(4/5(4/5-3/5)(4/5-5/8)(4/5-3/8))`


`A=sqrt(4/5*1/5*7/40*17/40) =sqrt(119/10000)`


`A=sqrt119/100`


Thus, the area of the triangle is  `sqrt119/100`  square units.

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