Square When the circumference of a rectangle and a circle is equal, the method of deriving the area

Solution: Let the circumference be x, and assume that the length of one side of the rectangle is x 4-a(a>0), then:

The square area is (x 4) 2=x 2 16;

The area of the rectangle is (x 4-a) * (x 4 + a) = x 2 16-a 2;

The area of the circle is *r*r= *(x 2 ) 2=x 2 4 ;

a>0 => A 2>0 => A 2-A 2>0-A 2 => x 2 16> x 2 16-A 2 => square area》 rectangular area;

4 = > 1 >1 4 = > 1 * x 2 4>1 4*x 2 4 = > area of a circle》 square area.

Square area: area of a circle = (1 4 * x 2 4) :( 1 * x 2 4) = 1 4:1 = :4

Let the side length of the square be x

The radius of the circle is y

Square circumference = 4x

The circumference of the circle = 2 y

4x=2πy

x=πy/2

Square area = x 2

Area of the circle = y 2

Square Area Area of a circle = x 2 ( y 2) = ( y 2) 2 ( y 2) = 4

You can set the radius of the circle to be r and the side length of the square to x, so the perimeter is 4x and the area is s=x 2

Because the circumference of the square is equal to the circumference of the circle, the circumference of the circle is 4x, i.e. 4x=2*, so r=2x, so the area of the circle, s'=

So get s s'=

The circumference of the square is 4a=c

a=c4 circular circumference 2 r=c

r=c/2π

Area: s positive = a 2 = c 2 16

s circle = r 2 = c 2 4

So the area ratio is 4 16 = 4

Then the ratio of the area of the square to the circle is 4

The side length of the square of Shivu rock is envy a, and the radius of the circle is r

Then 4a=2 r, so a= r2

So the area ratio is a2: r2= 4

Because the circumferences are equal, the side length of the square a is c 4, and the radius of the circle is c 2 pai, so the square area is 16 c squared, and the circle area is pai multiplied by the square of c 4 times pai, and the ratio is simplified to get 4 pai

Let the perimeter be s

Square area = (s 4) 2

The radius of the circle r=s 2

Circular area = (s2) 2

The ratio of the square and circle area = (s 4) 2 (s 2 ) 2 = 4

Summary. Square Perimeter = 4 Side Length, Side Length = Perimeter 4, Area = Side Length Square = Perimeter Perimeter 16, Circumference = 2 Radius, Radius = Perimeter 2 , Circle Area = Radius Square = Perimeter Perimeter 4 , so the square to circle area ratio = 4

If the circumference of the square and the circumference of the circle are equal, then what is the ratio of the area of the square to the area of the circle? Why?

Square Perimeter = 4 Side Length, Side Length = Perimeter 4, Area = Side Length Square = Perimeter Perimeter 16, Circumference = 2 Radius, Radius = Perimeter 2 , Circle Area = Radius Square = Perimeter Perimeter 4 , so the square to circle area ratio = 4

Why is the area of a circle equal to the circumference * perimeter 4 factions?

That's the explanation.

I didn't get it.

Circumference c square side length = 1 4c

Square area = (1 4c0 2 = 1 16c 2 radius of a circle = c

Circle area = circle area: square area = 1:1 16c 2 = 16::

Solution: Let their circumference be 1

When the circumference of the square and the circle are equal, it can be calculated that the area of the circle is larger than the area of the square.

Let the perimeter be s, then the area of the square is (s 4) 2, and the area of the circle is (s 2 ) 2, so the area of the circle is a multiple of the area of the square.

You can set the radius of the circle to be r and the side length of the square to x, so the perimeter is 4x and the area is s=x 2

Because the circumference of the square is equal to the circumference of the circle, the circumference of the circle is 4x, i.e. 4x=2*, so r=2x, so the area of the circle, s'=

So get s s'=

If the circumference of a circle is equal to the circumference of a square, then the ratio of the area of the circle to the area of the square is 4

then square. The area is 1

The circle area is. pi*r^2

pi*(4/2pi)^2

4/pi

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Let the perimeter be x square side length = x 4, area = (x 4) = x 16 circle radius = x 2, area = (x 2 ) = x 4 The ratio of the two = x 16: x 4 = :4

Ask what is the ratio of the area of a circle, square, and rectangle with equal circumference.

What is the ratio of the area of a circle, a square, a rectangle with equal circumference.

The ratio of their areas is: 4:3 rectangles, when the circumference of the square and the circle are equal, the area of the circle is the largest, the area of the square is centered, and the area of the rectangle. Least.

Ask how it was calculated.

What is the area ratio of a circle, a square, a rectangle with an equal circumference and how to calculate.

Answer: Let the circumference be 4a, then the side length of the square is a, and the area a 2 is the radius of the circle r, 2 r=4a, r=2a The area is (2a) 2=4a 2 s, and the circle of s = a 2 (4a 2 )= 4

Rectangle: If the length is x, the width is 4a 2-x, the area is x(4a 2-x) =-(x-4a 4) 2+4a 2 16, and the maximum area is 4a 2 16

Square: The side length is a, the area is 4a 2 16 circle: the radius a 2 , the area is a 2 So the ratio of the area is: 4:4

The previous answer was a little wrong.

Let the circumference be c, the radius of the circle is r=c 2, the area of the circle is s, the circle = r =c 4, the side length of the square is a=c 4, and the area of the square is s=a =c 16, then the s is positive scircle=(c 16) (c 4 )= 4

Let the side length of the square be x and the radius of the circle be r.

Circumference equal: 4x=2 r

x=1/2∏r

Area ratio: x2: r2

1/4∏2r2:∏r2=∏:4