If the area of the inscribed circle of a square is 154 cm², then the area of a square is :

1. 190 cm²

2. 192 cm²

3. 196 cm²

4. 198 cm²

ABCD is a square with inscribed circle having radius 'r' and center O.

Given,

Area of circle = 154 cm².

We know that,

$\text{Area of circle} = πr^2 \\[1em] \Rightarrow πr^2 = 154 \\[1em] \Rightarrow \dfrac{22}{7} \times r^2 = 154 \\[1em] \Rightarrow r^2 = \dfrac{154 × 7}{22} \\[1em] \Rightarrow r^2 = 49 \\[1em] \Rightarrow r = \sqrt{49} = 7 \text{ cm}.$

For a circle inscribed in a square,

Diameter of circle = Side of square

Side = 2r = 2 × 7 = 14 cm.

Area of square = (side)²

= (14)²

= 196 cm².

Hence, option 3 is the correct option.