Question

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

Answer 1

`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`

Answer 2

`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"`