Find the area of a quadrilateral `A B C D` in which `A B=42 m ,B C=21c m ,C D=29 c m ,D A=34 c m` and diagonal `B D=20 cm`

Explanation

Area of `/_\ ABD=sqrt(s(s-a)(s-b)(s-c)`
`s=1/2(a+b+c)`
`s=(42+20+34)/2=48cm^2`
Area of `/_\ ABD=sqrt(48(48-42)(48-20)(48-34)`
`s=sqrt(48xx6xx28xx14`
`s=sqrt112896`
`=336cm^2`
Now in`/_\ BDC,s=1/2(21+20+29)=35cm`
Area of `/_\ BDC=sqrt(35(35-29)(35-20)(35-21)`
`=>sqrt(35xx6xx15xx14)`
`=>sqrt44100=210cm^2`
area of a quadrilateral `A B C D=336+210=546sm^2`