Question

Find the area of the shaded region in the following figure, if AC = 24 cm, BC = 10 cm and O is the centre of the circle. (Use π = 3.14)

 

Answer 1

It is given a triangle ABC is cut from a circle.

`AC=24 cm `

`BC=10 cm`

`"Area of ΔABC=1/2 ACxxBC"`

                    ` = 1/2xx24xx10`

                     `=120 cm^2`

In ΔABC,

`∠ACB`, Since any angle inscribed in semicircle is always right angle.

By applying Pythagoras theorem,

`AB^2=AC^2+BC^2`

`=24xx24+10xx10`

`=576++100`

`=676 cm^2`

`OA=AB/2`

`=26/2 cm`

`=13 cm` 

We know that the area A of circle of radius r is 

`A=pi r^2

`Substituting the value of radius r,

`A=3.14xx13xx13`

`= 530.66 cm^2`

Area of semicircle=`1/2 pir^2`

                         ` =530.66/2 cm^2`

                          ` =265.33 cm^2`

`"Area of shadded region=Area of semicircle-Area of triangle" `

`=530.66-265.33-120`

`= 145.33 cm^2`