Question

Периметр квадрата равен 32 корень из 3 . определите площадь круга описанного около квадрата

Answer 1

Сторона квадрата а=(32*√3)/4=8√3, радиус описанной окружности R=диаметру квадрата/2=(√(а²+а²))/2=(√2а²)/2=а/√2,
Sокр=pi*R²=pi*a²/2=pi*(64*3)/2=pi*32*3=96*pi ≈ 301,44

Answer 2

Perimeter of the Square

To find the perimeter of a square, we need to know the length of one side of the square. In this case, the perimeter of the square is given as 32√3.

Let's denote the length of one side of the square as s. The formula for the perimeter of a square is 4s.

Therefore, we can set up the equation 4s = 32√3 and solve for s.

To solve this equation, we can divide both sides by 4:

s = (32√3) / 4

Simplifying the right side of the equation:

s = 8√3

So, the length of one side of the square is 8√3.

Area of the Circle Inscribed in the Square

To find the area of the circle inscribed in the square, we need to know the radius of the circle. The radius of the circle is equal to half the length of one side of the square.

In this case, the length of one side of the square is 8√3. Therefore, the radius of the circle is (8√3) / 2 = 4√3.

The formula for the area of a circle is πr^2, where π is a mathematical constant approximately equal to 3.14159 and r is the radius of the circle.

Substituting the value of the radius into the formula, we get:

Area = π(4√3)^2

Simplifying the expression inside the parentheses:

Area = π(16 * 3)

Multiplying:

Area = 48π

Therefore, the area of the circle inscribed in the square is 48π.

Please note that the exact value of π is an irrational number and cannot be expressed as a finite decimal. It is commonly approximated as 3.14159.

I hope this helps! Let me know if you have any further questions.