Question

Find the area of the shaded region in the given figure.

 

Answer 1

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

`AB^2=12^2+16^2`

`AB^2=144+256`

`AB=sqrt400`

`AB=20cm`

∴ Area of triangle = `1/2xxADxxBD`

`=1/2xx12xx16`

`=96cm^2`

Now 

In ΔABC, S =`1/2(AB+BC+CA)`

`=1/2xx(52+48+20)`

`1/2(120)`

`60cm`

By using heron’s formula
We know that, Area of Δle ABC `=sqrt(s(s-a)(s-b)(s-c))`

`=sqrt(60(60-20)(60-48)(60-52))`

`=sqrt(60(40)(12)(8))`

`=480cm^2`

`Area of shaded region = Area of ΔABC – Area of ΔADB`

`=(480-96)cm^2`

`384 cm^2`

∴ Area of shaded region = 384 `cm^2`