Question

Two regular polygons of same sides 40cm and 9cm in length of the side of another polygon for the same no. sides and whose area is area equal to the sum of the areas of the given polygons in cm

Answer 1

The area of the regular polygon is proportional to the square of the side and the number of sides in the polygon.

The formula for the area of a regular polygon of 'n' sides
$\Delta_n=\frac{1}{4}n\ a^2\ Cot\frac{\pi}{n}$

Let the length of the regular polygon we want be x cm.   Applying this formula:
 
   n/4 * 40² * Cot(π/n)  +  n/4 * 9² * Cot(π/n) =  n/4 * x² * Cot(π/n)

=>   x² = 40² + 9² = 1681
       x = 41 cm        answer.