Question

The area of the circle and the area of a regular polygon of n sides, and of perimeter equal to that of the circle are in the ratio of

• A. tan$\left( \frac { \pi } { 3 } \right)$: $\frac { \pi } { \mathrm { n } }$
• B. cot : $\frac { \pi } { \mathrm { n } }$
• C. sin: $\frac { \pi } { \mathrm { n } }$
• D. cos : $\frac { \pi } { \mathrm { n } }$

Answer 1

Answer: (A)

tan$\left( \frac { \pi } { 3 } \right)$: $\frac { \pi } { \mathrm { n } }$

Answer 2

The perimeter of a regular polygon of n sides

= 2nr sin

If the radius of the circle is a then 2pa = 2nr sin ... (i)

Now area of polygon = n

̃ ratio of areas of circle and polygon

= =: (from (i)