Question

The given diagram comprises of two sectors with angles 30º and 60º, their radii are 7 cm and 14 cm respectively. Both have center O. The perimeter of the shaded region is

(a) \(54 \frac{1}{3}\) cm  

(b) 105 cm 

(c) \(46 \frac{1}{3}\) cm 

(d) 77 cm

Answer 1

Answer : (c) 46 \(\frac{1}{3}\) cm

∴ Required perimeter = AB + arc length BC + CD + arc length DE + AE

= 14 + \(\frac{60}{360}\) × 2 × \(\frac{22}{7}\) × 14+ 7 + \(\frac{30}{360}\) × 2 × \(\frac{22}{7}\) × 7 + 7

= 28 + \(\frac{44}{3}\) + \(\frac{11}{3}\)

= 28 + \(\frac{55}{3}\) 

= \(\frac{139}{3}\)   

=  46 \(\frac{1}{3}\) cm