Question

Construct a regular pentagon inside a circle of radius $6cm$. The length of each side of the pentagon is: (approx.)

• A. $6cm$
• B. $7cm$
• C. $8cm$
• D. $9cm$

Answer 1

The correct option is B $7cm$

Each side of the pentagon makes an angle x at the center

$⟹5x=360$

$x=72$

Now lets consider side AB which is a chord to the circle

Let OP be a perpendicular to AB

$⟹AP=BP⟹AB=2AP$

IN $△OAP$

$\angle OPA=90$

$\angle POA=\frac{x}{2}=\frac{72}{2}=36$

$\sin 36=\frac{AP}{OA}$

$AP=0.6\times 6=3.6$

$AB=2\times 3.6=7cm$