What is the area of the square (in cm²) whose vertices lie on a circle of radius 5 cm?

50

We know that,

Diagonal of a square = \(\sqrt {2}\)(side)

Area of a square = (side)² 

We have,

The radius of the circle = 5 cm

 Diameter of the circle = Diagonal of the square

Diameter = 10cm

10 = \(\sqrt {2}\)(side)

side = 5\(\sqrt {2}\)

Now, the area of the square = (5\(\sqrt {2}\))²

= 50 cm²