The area of a square is 900 cm². Its perimeter is equal to the perimeter of a regular hexagon. What is the area in cm² of the hexagon?

Correct option is B

Given:

Area of square =$$900cm^2$$​​

Perimeter of square = Perimeter of hexagon

Formula Used:

Area of hexagon =$$\frac{3\sqrt{3}}{2} a^2$$​​

Solution:

Area of square =$$a^2 = 900cm^2$$​​

​$$a= \sqrt{900}$$​​

a= 30cm

Let the side of hexagon be x

Then perimeter of square = perimeter of hexagon

​$$4 \times 30$$​ = 6x

x= 20cm

Area of hexagon =  $$\frac{3\sqrt{3}}{2} (20)^2$$​​

​$$= 600\sqrt{3}cm^2$$​​