Question

Find the area of a quadrilateral ABCD in which AB = 42 cm, BC = 21 cm, CD = 29 cm, DA =34 cm and diagonal BD =20 cm.

Answer 1

Given that
Sides of a quadrilateral are AB = 42 cm, BC = 21 cm, CD = 29 cm
DA = 34 cm and diagonal BD = 20 cm
Area of quadrilateral = area of ΔADB + area of ΔBCD.
Now, area of ΔABD
Perimeter of ΔABD
We know that

⇒ S = `1/2`(𝐴𝐵+𝐵𝐷+𝐷𝐴)
= `1/2`(34+42+20)=96
=`96/2`
= 48 𝑐𝑚

Area of ΔABD = `sqrt(S(S-AB)(S-BD)(S-DA))`

`=sqrt(48(48-42)(48-20)(48-34))`

`=sqrt(48(14)(6)(28)`

`=336cm^2`

Also for area of ΔBCD,
Perimeter of ΔBCD

`2s = BC + CD + BD`

`⇒S=1/2(29+21+20)+35cm`

By using heron’s formulae
Area of ΔBCD =`sqrt(s(s-bc)(s-cd)(s-db))`

`=sqrt(35(35-21)(53-29)(35-20))`

`=sqrt(210xx210)cm^2`

`= 210cm^2`

∴ Area of quadrilateral ABCD = 336 + 210 = 546 `cm^2`