Find the area of the shaded region in the given figure.
We are given the following figure with dimensions.
Area of shaded region = Area of ΔABC – Area of ΔADB
Now in ΔADB
`⇒ AB62 = AD^2 + BD^2` --(i)
⇒ Given that AD = 12 cm BD = 16 cm
Substituting the values of AD and BD in the equation (i), we get
∴ Area of triangle = `1/2xxADxxBD`
In ΔABC, S =`1/2(AB+BC+CA)`
By using heron’s formula
We know that, Area of Δle ABC `=sqrt(s(s-a)(s-b)(s-c))`
`Area of shaded region = Area of ΔABC – Area of ΔADB`
∴ Area of shaded region = 384 `cm^2`
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- Area of a Triangle by Heron's Formula