A square or a circle?

If the square has area 4, then it's side length must be the square root of that, which is 2. So, the diameter of the circle is 2, and hence it has radius 1. So the circle has area pi * 1^2 which is pi.

If the square has area 4, its side length is sqrt(4) = 2. So, the radius of the circle must be 2/2 = 1. Hence:

A(Circle) = (Pi)*(radius)^2 = Pi

$\boxed{\text{ Area of a SQUARE} = \text{side length}^2}$ *Note: we'll refer to the side length as $s$

$\boxed{\text{ Area of a CIRCLE} = \pi r^2}$

Given: $A_S = 4$ , then we can deduce from $\color{#0C6AC7} A_S = s^2$ that $\color{#E81990} s^2 = 4$ $\rightarrow$ $\color{#E81990} s = 2$

Since the circle is inside the square, we know that the circle is just as wide as the square. So, the diameter of the circle would be equal to the side lengths of the square:

• $\text{diameter } d = \text{ side length } s$

$\rightarrow d = 2$

• $\text{diameter } d= 2 \cdot \text{radius } r$

$\rightarrow r = 1$

So, since we know $r=1$ , we can plug that into the formula for the area of a circle, $\color{#0C6AC7} A_C = \pi r^2$ , to find the circle's area.

$\large{ \pi \cdot 1^2 = \pi \cdot 1 = \boxed{ \pi}}$