Question

A regular pentagon is drawn with all its vertices on a circle of radius 15 centimetres. Calculate the length of the sides of this pentagon.

Answer 1

Sum of angles of pentagon 

= (n – 2)180 

= (5 – 2)180 

= 540° 

One angle of regular pentagon = \(\frac{540}{5}=180^\circ\)

In figure ∠ABC = 108°

∠ABD = \(\frac{108}{2}=54^\circ\)

In right angled triangle BFO

cos 54 = \(\frac{BF}{OB}=\frac{BF}{15}\)

BF = 0.5878 x 15 = 8.817

AB = 2 x 8.817 = 1.7644

One side of regular pentagon = 1.7644 cm