Question

In the following figure, O is the centre of a circular arc and AOB is a straight line. Find the perimeter and the area of the shaded region correct to one decimal place. (Take π = 3.142)

 

Answer 1

(i) Let us find the perimeter of the shaded region.

`∴ "Perimeter"=pixx10+12+16`

`∴ "Perimeter"=3.142xx10+28`

`∴ "Perimeter"=31.42+28`

`∴ "Perimeter"=59.42`

Therefore, perimeter of the shaded region is  59.4cm.

Now we will find the area of the shaded region can be calculated as shown below,Area of the shaded region = Area of the semi-circle − area of the right angled triangle First, we will find the length of AB as shown below,

`AB^2=AC^2+CB^2`

`∴ AB^2=12^2+16^2`

`∴ AB^2=144+256`

`∴ AB^2=400`

`∴AB^2=20`

`∴"Area of the shaded region" =(pixx10xx10)/2-1/2xx12xx16`

`∴"Area of the shaded region"=pixx50-6xx16`

`∴"Area of the shaded region"= pixx50-96`

Substituting pi=3.142 we get,

`∴"Area of the shaded region"=3.142xx50-96`

`∴"Area of the shaded region"=157.1-96`

`∴"Area of the shaded region"=61.1`

Therefore, area of the shaded region is `61.1 cm^2`