Question

If the area of the regular pentagon is $\frac{20}{\surd (5-2\sqrt{5})}$ cm${}^2$, then the length of each side of polygon is -

• A. 4 cm
• B. 6 cm
• C. 7 cm
• D. 8 cm
• E. 5 cm

Answer 1

The correct option is A

4 cm

Area of a regular pentagon of side length `a' m

= $\frac{\sqrt{5(5+2\sqrt{5})}}{4}$ a${}^2$

$\frac{\sqrt{5(5+2\sqrt{5})}}{4}$ a${}^2$ = $\frac{20}{\surd (5-2\sqrt{5})}$

$\therefore$ a = 4 cm