Question

Find the perimeter of the given figure , where O is the centre of the given sector ​

Answer 1

first find the perimeter of full circle that is

$2\pi \times 42$

and then subtract the area of sector from it

Answer 2

The perimeter of the given figure is 282 cm.

Explanation:

As per given figure , We have a circle with center O and radius 42 cm.

Circumference of circle = $2\pi r= 2(\dfrac{22}{7})(42)=264\ cm$

Perimeter of the given figure  =  Circumference of the circle - (length of arc AB) + 2 (radius )

For arc AB , Central angle = 90°

Length of arc  = $\dfrac{x}{360}\times (\text{Circumference of circle})$ , where x is central angle.

Length of arc AB = $\dfrac{90}{360}\times264=66\ cm$

Now , Perimeter of the given figure  = 264 cm - 66 cm +2(42) =282 cm

Hence, the perimeter of the given figure is 282 cm.

# Learn more :

In given figure, find angle POB where O is the centre of the circle.​https://brainly.in/question/13750128