In a triangle, the sides are given as `11 cm, 12 cm` and `13 cm.` The length of the altitude is `10.25 cm` corresponding to the side having `12 cm.`

Answer

1

Explanation

Since the sides of a triangle are `a = 11 cm, b=12 cm` and `c=13 cm.`
`"Now, semi-perimeter, " s=(a+b+c)/(2)`
`=(11+12+13)/(2)=(36)/(2)=18cm`
`"Area of a triangle " =sqrt(s(s-a)(s-b)(s-c))" "["by Heron's formula"]`
`=sqrt(18(18-11)(18-12)(18-13))`
`=sqrt(18xx7xx6xx5)`
`=sqrt(3xx6xx7xx6xx5)`
`6=sqrt(3xx7xx5)`
`6=sqrt(105)=6xx10.25`
61.5 `cm^(2)`
`therefore" ""Area of" triangleABC=(1)/(2)xxBCxxAD" "[because"area of triangle"=(1)/(2)("base"xx"height")]`
`=(1)/(2)xx12xx10.25=6xx10.25=61.5 cm^(2)`