Find the area of a square circumscribed around a circle of radius 4.

Let’s figure out which geometric figure is called a square
A square is a quadrilateral in which all sides are equal and the corners are straight.

Let’s write a formula for calculating the area of ​​a square
S = a²,

where S is the area of ​​the square, and is the side of the square.

To find the area of ​​a given square, you need:
find the side of a square
substitute the value of the side of the square in the formula
make calculations;
Let’s make a drawing of a square circumscribed around a circle.

Looking at this figure, we see that the side of the square circumscribed around the circle is equal to the diameter of the circle.

D = a.

where D is the diameter of the circle, a is the side of the square,

In the problem statement, we are given the radius of the circle

Find the diameter of the circle (side of the square)
The diameter of a circle is equal to twice its radius. Let’s write down the formula for calculating the diameter of a circle:

D = 2 × r,

where r is the radius of the circle.

D = 2 × 4 = 8.

This means that the side of the square is 8 units.

Calculate the area of ​​the square
S = a² = 8² = 64 sq. units

Answer: the area of ​​the square is 64 sq. units