Question

Figure shows a regular pentagon with all of its vertices on the sides of a rectangle. If $BC=\frac{1}{4}$, calculate the perimeter of the pentagon.

• A. $0.31$
• B. $0.62$
• C. $0.77$
• D. $0.80$
• E. $1.00$

Answer 1

The correct option is C $0.77$

The vertex angle of pentagon is $108$ degrees.
Let the length of side of pentagon be $a$ , by sine rule we get
$\frac{a}{\sin 90}=\frac{1/8}{\sin 54}$, which gives $a=0.1545$
Perimeter of pentagon is $5\times 0.1545=0.77$.