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.
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)
= 48 𝑐𝑚
Area of ΔABD = `sqrt(S(S-AB)(S-BD)(S-DA))`
Also for area of ΔBCD,
Perimeter of ΔBCD
`2s = BC + CD + BD`
By using heron’s formulae
Area of ΔBCD =`sqrt(s(s-bc)(s-cd)(s-db))`
∴ Area of quadrilateral ABCD = 336 + 210 = 546 `cm^2`
Concept: Area of a Triangle by Heron's Formula
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