Question

A chord of a circle of radius 14 cm subtends an angle of 90° at the centre. Find the perimeter of the shaded region. (Use `sqrt(2)` = 1.41)

Answer 1

Given: Radius of circle (r) = 14 cm

Sector angle (O) = 90°

To find: Perimeter of shaded region.

In right angle ΔAOB

OA = OB = 14 cm   ...(Radius of circle)

By Pythagoras theorem,

(AB)² = (OA)² + (OB)²

⇒ (AB)² = (14)² + (14)²

⇒ AB² = 196 + 196

⇒ AB² = 392

⇒ AB = `sqrt(392)`

⇒ AB = `14sqrt(2)` cm

⇒ AB = 14 × 1.41   ...`(∵ sqrt(2) = 1.41)`

⇒ AB = 19.74 cm

Length of arc ACB = `θ/(360°) xx 2πr`

= `(90°)/(360°) xx 2 xx 22/7 xx 14`

= `1/4 xx 4 xx 22`

= 22 cm

Perimeter of shaded region = AB + arc ACB

= 19.74 + 22

= 41.74 cm