Two regular polygons have the same number of sides. Their lengths are in the ratio 7 : 5 and the area of the larger polygon is 1127 $$\text{cm}^2$$​. Find the area of the smaller polygon.

Correct option is A

Given:
Two regular polygons have the same number of sides.
The ratio of their side lengths is 7 : 5 .
The area of the larger polygon is $$1127 \, \text{cm}^2$$​

Solution:
Let the side length of the larger polygon be  7x and the side length of the smaller polygon be  5x .
The ratio of their areas is:
$$\left( \frac{7x}{5x} \right)^2 = \left( \frac{7}{5} \right)^2 = \frac{49}{25}$$​​

Let the area of the smaller polygon be A . Then:

$$\frac{1127}{A} = \frac{49}{25}$$​​

A =$$\frac{28175}{49} = 575 \, \text{cm}^2$$​