The area of a regular polygon of `n` sides is (where `r` is inradius, `R` is circumradius, and `a` is side of the triangle (a) `(n R^2)/2sin((2pi)/n)` (b) `n r^2tan(pi/n)` (c) `(n a^2)/4cotpi/n` (d) `n R^2tan(pi/n)`

Options

A. `(nR^(2))/(2) sin ((2pi)/(n))`
B. `nr^(2) tan ((pi)/(n))`
C. `(na^(2))/(4) cot.(pi)/(n)`
D. `nR^(2) tan((pi)/(n))`

Answer

A, B, C

Explanation

Area of polygon `= nxx` Area of `DeltaOBC`
`=(na^(2))/(4) "cot:(pi)/(n)`..(i)
Now, `a = 2r "tan" (pi)/(n)`
`rArr` Area of polygon `= nr^(2) tan ((pi)/(n))` [from Eq. (i)]
Also, `a = 2R "sin" (pi)/(n)`
`rArr = (nR^(2))/(2) sin ((2pi)/(n))` [from Eq. (i)]