Find the area of triangle abc if a=11, b=9, c=5?

2 Answers
maganbhai P.
Mar 7, 2018

#22.19#

Explanation:

We know that area of #triangleABC=triangle=color(red)(sqrt(s(s-a)(s-b)(s-c))#
where,#2s=a+b+c#.
Taking, #a=11,b=9,c=5#,we have,#2s=11+9+5=25rArrs=12.5#
#triangle=sqrt(12.5(12.5-11)(12.5-9)(12.5-5))#
#=sqrt((12.5)(1.5)(3.5)(7.5))~~22.19#

Ujjwal
Mar 7, 2018

#22.16 " cm"^2#

Explanation:

Use the Heron's formula to find the area of the triangle.

According to Heron's formula ,

Area of triangle #= sqrt[S(S-a)(S-b)(S-c)]#

Here , #S = "Semiperimeter of" triangleabc#

#=> (a+b+c)/2#

#=> (11+9+5)/2#

#=> 25/2 "cm"#

And #a=11" cm"#

#b=9" cm"#

#c=5" cm"#

Put these values in the herons formula.

#=> sqrt[25/2(25/2-11)(25/2-9)(25/2-5)]#

#=> sqrt[25/2xx3/2xx7/2xx15/2#

#=> sqrt(5/2xx5/2xx3/2xx3/2xx5xx7#

#=> 5/2xx3/2xxsqrt(5xx7#

#=> 15/4xxsqrt35#

#=> 3.75sqrt35#

#=> 3.75xx5.91#

#=> 22.1625" cm"^2#

#=> 22.16 " cm"^2 "approximately"#

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